There's a lot of analysis to be done for this game, and the page is very incomplete for now. Unmarked spoilers follow.
The story follows the main character through the four stages of Jungian individuation:
ShadowThe Shadows, of course.
Anima/AnimusElizabeth (and Theo) serve this purpose. It helps that they help the main character access their various Personas.
ManaThe Mana figure is supposed to be either a wise old man or a mother, and Nyx Avatar counts as both — Nyx is the maternal being, after all, and Nyx Avatar gives the main character wise speeches on the nature of the Arcana and life.
IndividuationThe encounter with the Mana, Nyx Avatar, leads the main character into the final stage of individuation, where his various Personas and Arcanas (in the form of Social Links) come together to make the Universe Persona. (This is why the main character only obtains the Universe after that battle, when it seems to serve no purpose at all).
The Fool's JourneyThe Fool's Journey is the subject of Mr. Edogawa (the school nurse)'s biggest speech, so you know it's important. It's why the main plotline is called The Journey in FES, and it shows up in several parts of the game: the main cast, Personas, Shadows, and Social Links. Most of the game focuses on a subset of the Fool's Journey, from Fool through Death.
The main cast
Every Persona-user in the game (except Elizabeth) is associated with one of the first 13 Arcanas in the Fool's Journey, based on their Persona's assigned Arcana. If you also count Ryoji, this covers the entire portion the game focuses on (from Fool through Death).
Fool: Main CharacterThe Fool represents a blank state. Notably, the character can use any Persona and his/her personality is what you make of it. Personality Blood Types (Type 0) hint that s/he's outgoing and optimistic but can be cruel and careless at times.
Magician: JunpeiThe Magician starts the Fool off on their journey, and Junpei comes to make friends with the MC right at the beginning of the game. His initial Persona, Hermes, is traditionally associated with that particular aspect of The Magician, since he leads Persephone (the goddess of spring) out of the Underworld in Ancient Greek mythology. Junpei is eager to fight Shadows, but is very immature. Only when Chidori sacrifices her life for his does his Persona evolve into Trismegistus, which is the portrayal of Hermes most strongly associated with the Magician traditionally.
Priestess: FuukaFuuka's role as the team's navigator and scanner plays into the High Priestess's themes of intuition and mystical visions. Her Persona is based off Saint Lucy/Lucia, a patron saint of the blind who continued to prophesise even after the emperor's guards cut her throat and gouged out her eyes. Fuuka's role as the "eyes" of SEES and her abilities in general relate to her. After determining that she wants to remain connected to all of her friends, especially the recently transferred Natsuki, her emotions give rise to Juno, queen of the Roman gods. This is likely to fit with the description of the Juno Moneta, known as "the one who warns". The High Priestess card can represent the ideal femininity and inner confidence, and in the Male Protagonist Route's Priestess Social Link, she's afraid of revealing her true self because she's ashamed of her fondness for computers and electronics (as she thinks it's an unfeminine hobby), so to avoid seeming unfeminine, she decides to get better at cooking, but eventually ditches it and realizes that being good at electronics and computers is not something to be embarrassed about.
Empress: MitsuruMitsuru is represented by the Empress Arcana. The Empress symbolizes feminine leadership, creation, sensuality, and abundance. Mitsuru is a well-off, sheltered corporation heiress, and since so much is expected from her, she's strict, but she means well and is very much the Team Mom. She expects SEES to maintain good grades, even signing them up for summer school. She is popular with both men and women at school. The protagonist may lead SEES in battle and in Tartarus, but out of those situations Mitsuru is the one that manages SEES, and has been doing so since a few years before the beginning of the game. In the Male Protagonist Route's Empress Social Link, he helps Mitsuru appreciate her life (despite her many responsibilities) and regain control of it.
Emperor: AkihikoAkihiko fulfills the role of the Emperor. The Emperor Arcana represents masculine leadership, so it's fitting that Akihiko's Persona is the first to evolve. However, the Emperor also represents dominance, power, and a desire for control. After the death of his sister, Akihiko became obsessed with getting stronger, believing that he could protect anyone if he were just strong enough. It isn't until Shinjiro's death that Akihiko realizes what he needs to do.
Hierophant: ShinjiroShinjiro serves the role of the Hierophant by guiding the rest of SEES: his death triggers Persona transformations in both Akihiko and Ken.
Lovers: YukariYukari, as the girl who could be considered the "canon" love interest, fits the Lovers Arcana. However, she also fits in that she has several choices to make. Should she forgive Mitsuru for keeping secrets? Should she forgive her mother for her behavior after her father's death? Should she continue to believe in her father while knowing that he's responsible for unleashing the 12 Arcana Shadows on the world?
Chariot: AigisAigis is represented by the Chariot because of the process of her humanization (see Plato's Chariot Allegory, an allegory of the human soul). She slowly asserts herself as an individual, rather than a simple Anti-Shadow weapon. This is reflected in the contrast between her initial Persona's appearance and that of her evolved one, going from a Persona that is essentially a humanoid mask on a mechanical spine to a fully-human figure.
Justice: KenKen's Persona, Nemesis, represents absolute justice, or rather retribution. Ken himself illustrates the Justice Arcana very clearly. He joined SEES in order to seek revenge on Shinjiro for his mother's death. The question remains, however, whether or not it is right to seek revenge. Ken's desire for revenge is self-destructive, consuming most of his life, and he even plans to kill himself after taking revenge. This is another facet of Nemesis: she is a daughter of Nyx, and thus embodies a desire for death. When the crucial moment comes, Shinjiro refuses to take the role of Ken's enemy — he doesn't resist Ken, even giving his life to save him, but he does advise him against revenge for Ken's own benefit.
Shinjiro's influence as the Hierophant causes Ken to rethink his desire for revenge, and Nemesis evolves into Kala-Nemi. Kala-Nemi in the official works is stated to have been a pre-Vedic deity whose name means "wheel of time"; however, Vedic Sloka, or epic prayers, depict him not as the Wheel of Time itself, but its destroyer, one who frees people from ignorance, karma and the cycle of reincarnation. Kala-Nemi in another interpretation is depicted as a demon who wielded enough power to wage successful war against the gods — this would make sense when taking into consideration Ken's resolve to defeat the undefeatable avatar of death, ending the cycle of revenge once and for all.
Hermit: JinNot unlike the Hermit Social Link, Jin is referenced multiple times as an internet dweller, with Fuuka going so far as to say he's well-known on the internet at large, which helped him get the ball rolling on the Cult of Nyx. He's Takaya's right hand man and voice of reason, but eternally loyal to him for "showing him the way out of darkness". This can refer to the Hermit representing philosophical searches and introspection. The Hermit also represents guidance, which can refer to both Takaya's role to him or Jin directly influencing people to join the cult. His Persona, Moros, is the brother of Hypnos and Thanatos. He is the spirit who warns people of the day of their death, which is precisely what Jin himself does in the creation of the cult.
Fortune: TakayaTakaya's Persona, Hypnos, is the personification of sleep, brother of Moros and Thanatos and, most importantly, a son of Nyx. Fortune is an Arcana of fate and omnipotent forces, which makes sense, as Takaya welcomes the coming of Nyx on the promised day, and understands it is humanity's want of death that calls her to them. Fortune also advises to seize and make the most of your opportunities, which makes sense when you remember that Takaya sees Tartarus and the Dark Hour as one great opportunity, a "frontier which only a chosen few can explore".
Strength: KoromaruStrength is a card representing self-control, stability, and inner strength. He is fiercely loyal to both his late owner and SEES, protective of both the site of the priest's accident and his friends. This is shown in his Persona, Cerberus. Just as Cerberus watches over the gates of Hades, the Underworld in Ancient Greek mythology, Koromaru watches over the site of his master's death. From a gameplay perspective, Koromaru's Arcana also comes into play, as his Persona has no ascended form. Rather, his Persona has attributes of one that has already upgraded. Since the other members of the party only obtain their ascended Personae after sorting through some emotional baggage and/or rethinking their reasons for doing what they do, it seems to imply that Koromaru is already of sound mind and reason. Which, as representative of the card of inner strength and discipline, makes perfect sense.
Hanged Man: ChidoriThe Hanged Man symbolizes self-sacrifice, which obviously fits Chidori as she sacrifices her own life in order to save Junpei's. However, the Arcana can also symbolize surrendering your ego in favor of embracing new points of view, such as how she gains a new outlook on life since meeting and falling in love with Junpei. Her Persona, Medea, the daughter of King Aeetes, a sorceress who fell in love with Jason (of Jason and the Argonauts fame) and betrayed her father by not only aiding Jason, but running off with him. This mirrors Chidori's betrayal of Strega to save her own love.
Main character's PersonasThe progression through the Arcanas as the main character goes through different Personas is another Fool's Journey, if not a strictly linear one. Still, as the player progresses through the game, they'll tend to fuse Personas of higher-numbered Arcanas: low-numbered Arcanas tend to have lower-level Personas than high-numbered ones. In fact, the highest-level Magician and Emperor Personas have lower levels than the lowest-level Judgment and Aeon Personas.
Since one's Personas are tied to one's self, this makes the Fool's Journey a journey of self-discovery for the main character, and it closely ties it into the process of individuation. The final steps of both processes are the same; see the section on The World below.
Magician: Kenji TomochikaKenji's Social Link revolves entirely around his plan to get in a relationship with one of his teachers, Emiri Kanou. Very early on, he discusses his plans openly with you, and makes it a point that he his determined to succeed, which plays into his arcana as the Magician is mainly a card of initiative and self-confidence. However, it soon becomes apparent that Kenji is simply fooling himself, as Emiri stops returning his calls, and rumors spread of her being forced to transfer to another city. Turns out it's because she already has a fiancé, and Kenji's attempts at romance are a nuisance at best. Kenji's delusions are the result of his refusal to accept the painful facts, a sign of immaturity and a major implication of his Arcana.
Magician: Junpei IoriJunpei's Social Link in the female protagonist route is how he cares for you. While his immaturity does come into play, such as when the action movie is also thought provoking, he shows his initiative when pictures of you in your gym clothes appear. He doubts himself as he believes that the Persona mission is the only thing going for him. However, you inspire him to put in some hard work and eventually, encourage him to allow himself to be serious at times. He also decides to be someone that you can depend on.
Priestess: Fuuka Yamagishi
Empress: Mitsuru Kirijo
Emperor: Hidetoshi OdagiriAs the head of Gekkoukan High's student disciplinary committee, Hidetoshi has a lot of authority in the schools. At the beginning of his search for the smoker, he tirelessly interrogated half the school in order to find the person and discipline him, which causes people to label him as a tyrant. However, he confides to the protagonist that he doesn't agree with the school's suggestion to expel the smoker and just want to give him a lecture since he believes that a punish that severe would not prevent that from happening again. Eventually, after the school suggests that he questions the protagonist, he gave up his college recommendation by making it clear that he doesn't see them as a suspect, preserving his one true friendship in school and made him realize how his method only cause the students to not trust him. Eventually, he became more tactful towards his approach and was able to find the smoker and use his authority to convince him not to do it again and gave him the lighter as proof, becoming a more understandable authority figure.
Hierophant: Bunkichi and MitsukoThe meat of this Social Link comes from the couple's struggle to keep a tree planted by their late son, who taught at the high school, from being chopped down. They see the tree as all they have left of him and represents his passion for teaching. A petition gets going to keep the tree from being removed, and eventually gets the school to leave the tree alone. However, upon learning that the tree's removal was to make room for another wing of the building, the two decide that they cannot hinder the education of children to fulfill their own selfish wishes, and not even their son, as a teacher, would want that. They allow the tree to be cut down, thankful for the protagonist's support and the support of their son's former students. The Arcana comes into play when one considers that the Hierophant is a card of both conservatism and education. Initially, they wanted to keep the status quo by fighting to keep the tree alive. But eventually, this desire is overridden by how much they value education, as their son no doubt did, which is why they allow change for the sake of bettering the school their son loved so much.
Lovers: Yukari Takeba
Chariot: Kazushi MiyamotoMuch like Female Protagonist and Rio Iwasaki, the Male Protagonist meets Kazushi by joining a sports club. Kazushi is very determined and does his sport with gusto, even wearing his workout clothes all the time so that he can be ready to practice at a moment's notice. Much to his chagrin, Kazushi is informed that he has a knee injury that could leave permanent damage to his leg. However, Kazushi is determined to keep going as part of a promise to his young nephew, who has similar problems, even keeping his injury secret from the rest of the team. Eventually, though, he comes clean and opts to have the surgery, choosing (out of his own free will) to go through rehabilitation with his nephew.
Chariot: Rio IwasakiRio Iwasaki is the captain of either the tennis or volleyball team. She is very serious about her sport, sometimes too serious. She can't comprehend the other girls' interest in group dates. As the Social Link progresses, we learn that Rio did not ask to be captain, but rather, the other girls voted her into it. Eventually, however, Rio's strictness leads the other girls to walk out. At some point, Rio realizes that she has feelings for her childhood friend, Kenji. When she and the other girls reconcile, they encourage her to confess her feelings. She looks to the Female Protagonist, who tells her that it is her decision. This is the cornerstone of the Chariot Arcana: victory, control, and asserting one's self. She confesses her feelings to Kenji and is turned down for reasons she already knows. She isn't unhappy, though. She has finally taken control of her own life. She becomes even more serious about her sport and expresses a wish to play it in college.
Justice: Chihiro FushimiChihiro, the student council's treasurer, was accused of misappropriating funds for the student council due to her lack of skills in math and her recent interest in getting a new manga. As a result, the entire school turned against her and throughout her social link, is trying to rationalize what has happened to the funds and try to clear her name through this miscarriage of justice. Once Mitsuru involves the protagonist into the investigation however, Chihiro decides to use her sense of justice to confront the teacher she gave the money to, eventually finding out that he spent it on a taxi, thus clearing her name and giving justice to the one who lost the money.
Justice: Ken AmadaMuch like Nanako Dojima, Ken has a very strong sense of right and wrong for his age. In the early stages of his Social Link, Ken is uncomfortable showing his childish side to the Female Protagonist. It isn't until Shinjiro shows him the truth that Ken becomes comfortable showing his vulnerable side to her. Still, he is unsure of whether or not to make his feelings known. After all, there is a six year difference between them. At some point, however, he realizes (with some prodding from the Female Protagonist) that it's just a six year difference and that it isn't necessarily wrong. After all, that's what the Justice Arcana embodies — right and wrong.
Hermit: Maya (AKA Isako Toriumi)The Hermit Arcana represents wisdom, solitude, and philosophical searches. Maya, the Protagonist's friend from Innocent Sin Online, is, in fact, his homeroom teacher, Isako Toriumi. She fits in that her only interactions with the Protagonist are over the internet, where her face cannot be seen. She also fits in that she is older than the Protagonist and thus, much wiser. She is worried when it announced that Innocent Sin Online is to be shut down, and decides to send the chat logs between herself and the protagonist in order to convince them to keep the game going. After reading over them, she decided that she didn't like the person she saw interacting with him, constantly bad mouthing others behind their backs behind a mask of anonymity. She thanks the protagonist for teaching her to be more thoughtful, and logs off permanently, but not before writing for him a confession of love in the sand in the virtual game they played.
Hermit: Saori HasegawaIn Saori's S-Link, the Hermit represents a person who hides himself from others and doesn't care about what others do or say about him. Saori is the oldest student of the school and is respected (well, practically feared) by all her classmates. She doesn't care about anything they say about her until she meets the Female Protagonist, when she gains some confidence. After an incident when her homeroom teacher found a magazine with her picture and an interview saying she was a femme fatale and all her classmates despise her, she gets enough courage to go to the Public Announcements room and tell everyone she was the girl in the picture but the interview was fake. Then, she decides to leave the school and thanks the FeMC for everything. In her epilogue, she sends a letter to the FeMC where she tells her life in her new school is good but that she'll never forget her, as she was her first true friend.
Fortune: Keisuke HiragaKeisuke is unsure of what he wants to do in the future. He doesn't want to be a doctor because his father expects him to be one, yet he's very well versed in medical terminology and fellow club members think of him as 'the doctor', much to his annoyance. He joins a club to do something that is his own thing without his father's influence. However, once Keisuke gets recognition, his father begins pushing him in that direction. His Social Link is of the Fortune Arcana because of the circumstances Keisuke finds himself in: he doesn't know what to do because neither choice seems to really come from him and are instead influenced by others. Incidentally, it's only by chance that Keisuke happens to be in the same place as two people who need immediate medical attention and it's those incidents that make him realize what he truly wants. Keisuke comes to the decision that, while he was raised with the expectation of becoming a doctor, that isn't why he is choosing to be one. Instead, it is genuine desire to help people that drives him. He quits his club to study for the entrance exam and thanks the MC for helping him realize this.
Fortune: Ryoji MochizukiRyoji's Social Link is both adorable and sad. He is drawn to the Female Protagonist without understanding why. The revelation that he Appriser of Nyx, and thus, destined to bring about the Fall on the world he loves crushes him. Although he was only with SEES for a short time (Easy Come, Easy Go as they say), he pleads with them to kill him, not wanting them to suffer when the Fall arrives and is dismayed when they choose to let him live. Still, he is grateful for the he spent with the Female Protagonist and leaves with a smile.
Strength: Yuko NishiwakiYuko Nishiwaki is the manager of the sports club you join and is something of a Team Mom. While she does a good job of taking care of the team, she herself is uncertain of what she wants to do with her future. A young boy she knows asks her to coach him and his friends so that they can race some older kids. Coaching the children helps her realize what she wants to be: an athletic trainer. They say the Strength Arcana represents power with reason, after all. What’s a better occupation for such a person than one who teaches others to be strong?
Hanged Man: MaikoMaiko, who the Protagonist meets at Naganaki Shrine, behaves cheerfully, but is in reality very torn up about her parents' impending divorce. Her parents aren't giving her a straight answer for why, and even lash out at her when she is too persistent. Maiko's life is slowly spiralling out of control, until finally she resolves to run away. After all, if her parents really care for her, they'll surely look for her, right? And when they do, they finally realize what their fighting has done to their daughter. They tell her the truth about why they are divorcing, and she accepts it, choosing to live with her mother, who she says will not be able to take care of herself without her there. She does this knowing that she will have to leave the Protagonist, who she has developed a crush on and promises to marry someday.
Death: PharosOne of the few social links that progress automatically is a very appropriate way of representing this card. Pharos is basically a harbinger of the Shadow Arcana, warning the protagonist about the coming of the full moon. While the death of these Shadows is a very simplistic way of representing Death, the end of his social link brings about changes to the plot as well as S.E.E.S. in moving forward and how to end the Dark Hour once and for all. More specifically, how the end of the Shadows marks the beginning of facing Strega directly and eventually, the inevitable arrival of Nyx.
Temperance: Andre Roland Jean Gérard (AKA Bebe)A Japanophile, Bebe moved to Japan to experience the culture there and was able to thrive in it despite being a foreigner. A bump in the road came when his aunt, the one who funded the transfer, passed away, he was forced by his uncle to go back to France. Deciding that making a kimono would convince his uncle to let him remain in Japan for his high school, he worked tirelessly by using his knowledge of Japanese culture with his own culture to create something that he was proud of showing. After learning the true reason he was able to go to Japan however, he decided instead to spread his experience there to his home town and keep the spirit of his experience in the country.
Devil: TanakaTanaka's social link starts with him swindling the protagonist with money even though he has so much that there is no reason to do that. Feeling a bit sorry for them though, he decided to take them under his wing to give them some business advice. While he has never gotten rid of his greediness even up to Persona 5, he at least realize, in his own twisted way, that it is okay to help out someone and still enjoy the perks of being the president of his own company.
Tower: MutatsuWhen the Protagonist first meets Mutatsu, he is everything a monk shouldn't be: drinking, smoking, and it's clear that he wouldn't back down in a fight. Mutatsu has been doubting the path he's taken in his life - his wife and son have left him and he has his doubts about being a monk. A Heroic BSoD, if you will. Through his interactions with the Protagonist, it becomes clear that he does miss his family and wants to see them again. Eventually, he resolves to hire a private detective to find them - and he does. He is finally able to reunite and reconcile with his family.
- More accurately, the resolution of Mutatsu's reunion with his family is never revealed, merely his decision to do so. As the Tower Arcana represents impending doom, it is actually far more likely that his family rejects his attempts to reconcile. This emotional disaster is the embodiment of the Tower Arcana, and accepting it and moving on is important in one's journey.
- Alternatively: the Tower can also represent a rude awakening and the collapse of the structures and beliefs upon which one has built the foundations of one's life. Mutatsu has experienced this already in the disillusionment with his prior life that led him to take up the priesthood, and the collapse of his marriage; he is now in a position in which he must either rebuild anew what he believes in a way that will work for him, or continue dwelling in his bitterness.