This character is the hero's good friend. The hero can fool around with him, go to the bar with him for a drink and talk about some good old man-business with him. Additionally, the character, being older (though mental age matters more than physical age) and wiser than the hero, also acts as a mentor to the hero in times of need or advice.
However, just because the Big Brother Mentor cares about the hero doesn't mean that he can't suddenly break out of his buddy personality and sock him in the jaw if he thinks he deserves it. He only wants the best out of the hero, but won't hesitate to educate him the hard way if the hero shows reluctance to learn or has a tendency to run headlong into danger. And his punches are hard. In essence, he's the ideal big brother figure who knows when to get friendly or strict.
In anime, this kind of character is often addressed as the more informal "Aniki" instead of "Onii-san".
Often, this character is doomed to die — both to bring the Hero out of the character's shadow, and to give the character an emotional buildup.
This is a subtrope of The Obi-Wan.
If he and The Hero are romantically involved, or just have enough Ho Yay, this can become Lover And Beloved. Differs from Aloof Big Brother in that the Big Brother Mentor doesn't have to be a literal big brother and actually gives a damn about his "little siblings" (Or shows it quite more often than a merely emotionally repressed Aloof Big Brother). Compare with the Stern Teacher, tough and strict but loved by everyone.
As Setsuna's sempai, Kira in Angel Sanctuary often acts that way towards him. Yue Katou too to some extent. Sara Mudou calls Setsuna "aniki," but towards his own sister he is more of a... oh well...
Roy Fokker in Macross / Robotech is maybe the Ur Example for anime. And midway through the series, he kicks it. Damn pineapple salad and inner bleeding.
Ozma Lee in Macross Frontier is ultimately played as a subversion of the archetype. He's an older mentor, and even flies Skull One, but it's usually the other characters who give the most useful advices, he's made lots of mistakes, and he completely fails to die, even when pineapples are involved.
An evil example comes in Part 5 with the two mafia members Pesci and Prosciutto. Pesci is the little brother and ironically like other mentors Prosciutto dies by getting run over by a train and getting lodged in the wheels before Pesci gets how to be a good mafia worker. Then he dies by getting his head unzipped from his body and thrown into a lake.
In Part 7, Gyro Zeppeli's position as Johnny's friend and a teacher could fit this trope as well.
In Fullmetal Alchemist, Hughes is Roy's Big Brother Mentor, hitting pretty much every single qualification for one listed above at some point. He is one year older, but he has a family whereas Roy doesn't, and thus a very different perspective on life. He has one notable moment of snapping out of his easy-going attitude.
In an evil example of this trope from the manga, Pride acts as this towards Wrath, the youngest of the Homunculi. This becomes quite ironic when you learn Pride masquerades as his son, Selim Bradley.
In the anime version of Planetes, Hakim Ashmead fills this role for Hachimaki, at least until his Heel Face Turn where he was revealed to be The Mole for the terrorist Space Defense Front. Their mentor, Gigalt Gangaragash, straddles the line between a Big Brother Mentor and an actual The Obi-Wan.
2 prominent pairs on Yu-Gi-Oh! GX: Sho adopts Judai as his "aniki," whom he prefers to his biological Aloof Big Brother (until Judai dumps him for Johan). Manjyome also looks up to Asuka's brother Fubuki. Though he does also call Fubuki shishou (master) as well as big brother. The big brother part seems to be more because of his crush on Asuka, since if he ever married her, they would *be* brothers.
In Mobile Suit Gundam SEED Destiny, Athrun Zala tries to do this for Shinn Asuka. It doesn't really work, as Shinn is too messed up to listen, and Athrun doesn't really have the people skills to pull it off.
Mobile Suit Gundam 00's Neil Dylandy aka the first Lockon Stratos was some kind of advisor to not only Setsuna but the most of CB. Even if he's dead he'll probably return as a spiritual advisor. Still, Tieria Erde seems to fit a bit better in the second season, even dealing some Bright Slaps when needed.
Also, Lyle, Neil's twin younger brother and the second Lockon isn't necessarily theBig Brother Mentor but has his moments as well, specially in episode 18 where he counsels two of his teammates when they had romantic problems.
And Gundam AGE gives us Woolf Ennacle playing the role for Flit Asuno and Flit's son Asemu. He survives the first season, then epically and tearfully kicks it in the second one.
Played straight and subverted in Mobile Fighter G Gundam. Argo Gulskii is the oldest, more mature of the Shuffle Alliance and plays the role straight towards Domon and Sai Saici, whereas Schwarz Bruder subverts it by being Domon and Rain's own BBM... and a clone of Domon's Aloof Big Brother Kyouji, who specifically created him with some DG cells and the dead body of the real Schwarz Bruder to play this role before he was fully brainwashed by the Devil Gundam.
Zoro, to Luffy. Given that he's the Lancer, and Fan Speak sometimes denotes him as the First Mate of the crew, he often steps in to help Luffy make the tough choices given Luffy's personality. This was especially obvious when Usopp temporarily left the crew and Zoro both supported Luffy's decision to fight Usopp and later forced him to wait for Usopp's apology when it became apparent that Usopp wanted to return to their crew.
Brock is this to Ash and anyone else who is in the main traveling group in the Pokémon anime.
In Pokémon Special, Green is this to Yellow in her arc. A female example would be Crystal, to Emerald.
England was this to America (and most likely to Canada too) in Axis Powers Hetalia. China is considered the older brother of the rest of the Asian countries, such as Japan, South Korea, Macau, Vietnam, Hong Kong and Taiwan, but except for Korea they don't always acknowledge as this.
And Switzerland dotes on his adorable adopted sister Liechtenstein.
Kenshiro towards Bat, as stated when he calls him his "irreplaceable little brother."
Also Toki and Raoh towards Kenshiro.
Bat to his fellow orphans.
Maiza Avaro to Firo in Baccano. Firo reminds Maiza of his younger brother and guides him into the Camorra, and fittingly enough, after devouring Szilard, Firo obtains Maiza's brother's memories along with those of Szilard's other victims.
Osamu, Kaga and Johji to Hayato in Future GPX Cyber Formula, Kaga in particular, since he helps Hayato hone his driving skills in a crash race. Also Lope to Hiyoshi, as he helps Hiyoshi to get back into racing again after leaving the Sugo team.
Sakuragi of Rainbow might as well be the king of this trope. Seriously, his nickname is even An-chan ("Bro").
Tiger & Bunny has an interesting example; instead of giving the protagonist a Big Brother Mentor, they made the protagonist himself play this role where a number of younger characters were concerned. It's even invoked in the third episode, where Kotetsu's boss suggests he take this approach with Barnaby.
Lloyd Alexander: He's young, so why don't you try to lead him? You've been doing this for much longer, after all.
Sora is this to Ikki in Air Gear, even going so far as to teach him how to properly utilize the Wing Road. This attitude changes when Sora announces his Face Heel Turn and reveals that he was using Ikki and helping him become better so that the Wind Regalia can be made for him to take. All of this is just step one of his plot to become Sky King. This quickly leads to Ikki having a Heroic BSOD moment.
Future Gohan is this to Future Trunks in Dragon Ball Z. Slightly less so in the main timeline to Goten and Present Trunks. Goku's best friend Krillin was this to Gohan.
Nail was also like this to Dende, even after Nail's fusion with Piccolo.
In Saint Beast, Goh is occasionally called "big brother" by Shin, Rey and Gai for being The Leader of their group.
Byakuya Kuchiki has become this to both his adoptive sister Rukia and his Number Two Renji in Bleach. Specially to Renji: Compare the totally cold and cruel order to deny him treatment in the Soul Society arc, to the pep talk he gives the other during Sasakibe's funeral and the actual concern he shows during the fight against As Nodt. It shows Byakuya's Character Development quite nicely right before he almost dies.
In A Cruel God Reigns, Lindon acts as this for Ian, giving him advice on how to deal with first getting Jeremy to confess (though not Mind Rape him like Ian would like), and later on how to deal with his romantic feelings for Jeremy.
Valentine also acts as a sort of Big Brother Mentor for Jeremy, despite being the same age, if not younger.
Reiner Braun from Attack On Titan. He's seen as something of an older brother to the entire 104th Trainee Squad, and becomes an important influence on Eren, helping shape him into a capable soldier. It ends up resulting in Eren noting that one of Reiner's mistakes as The Mole was teaching him to fight.
Due to the nature of its "legacy" focus on characters, these pop up quite often in the DCU:
Although it's a bit moot now that they're actually brothers, Richard "Dick" Grayson decided early on to take a more active role in the mentoring of the third Robin, Tim Drake, than he did with the second, and the two developed a sibling-like relationship in the process. This was so well-liked by fans that Nightwing writer Chuck Dixon chose to devote what is normally a landmark issue - #25 - of that series not to a major battle or character death, but to Tim and Dick discussing life, Batman, and Dick's seemingly endless parade of hot girlfriends for an entire issue.
Well they were doing that while blindfolded, fighting bad guys, on a moving train (I kid you not). So I guess that is the equal of talking about sports and girls while tossing the football around if you were raised by Batman.
Although he initially played the role of the older brother who didn't want to be around the younger one, Wally West eventually grew quite fond of Bart "Impulse / Kid Flash" Allen (who's technically his cousin, once removed).
Wonder Woman and Donna Troy refer to each other as sisters, although it's been a while since Donna's actually been mentored by Diana. Much like the Batman / Nightwing / Robin relationship above, however, Donna served as an older sister to the second Wonder Girl.
Damian Wayne also sees Dick Grayson like this, genuinely respecting him and Dick is one of the few people who believes in him and helps steer Damian in the right direction.
Wolverine to practically any younger female character. Most notably Kid Sidekicks Jubilee and Kitty Pryde. In Wolverine #16, a reporter is going around asking people what they think of Wolverine. Jubilee says he's an amazing big brother. Kitty takes it a little further — she admits that she'll probably never get married because she always compares the guys she meets to Wolverine, and they never measure up.
Ironically, Gambit is now this to Wolverine's clone/daughter X-23 in her solo self titled series. Although they are on more equal terms than some of the other examples.
Maid Man and Cyndablock act like this to Empowered, showing her that not all superheroes are assholes. That it's the transvestite and the literal blockhead who actually are nice to her must say something about how much being a low-tier superhero sucks.
Rainbow Dash behaves this way toward Medley in Ace Combat The Equestrian War. By the end, Rainbow herself admits that, to her, Firefly is like an older sister she never had.
In Ah! Archfall!, Jago is a literal version; his brother (Bob) is sent to him to learn anger management. Jago encourages him to learn how to control himself in a fight, eventually culminating in Bob's disastrous duel with Skuld, after which Jago delivers swift justice in a beating so severe that he BREAKS HIS OWN HAND in the process. He also secretly supports Bob's tentative relationship with Chrono, despite the fact that she is training to be a Valkyrie and must therefore remain celibate.
In Battleship, the main character Alex is a directionless loser who's all but forced into the military by his older brother in the hopes that it'll straighten him out. The older brother is succesful and straightlaced...and his death early on in the movie motivates Alex into becoming a better soldier.
Harry Potter has Sirius Black, his godfather, and Remus Lupin. Too bad that both of them die.
Seregil to Alec in Nightrunner, and also Micum and Beka to Alec at times.
This is Older Than They Think: In The Bible, when the archangel Raphael took a human form to find and fight the demon Asmodeous, he posed as a young man named Azariah who played this role for young Tobias, the youth who was qualified to marry Sarah, the girl whom Asmodeous lusted after and tormented by killing her husbands right after the wedding.
For the reader's enlightenment: this story is from the Book of Tobit, which is not considered part of the Bible by either Jews or non-Catholic/Eastern Orthodox Christians. Although it is still considered a useful read.
Jonathan can be considered this to David. He's at least some years older than David, and guides and protects him; he accepts that Jehovah has chosen David to succeed Saul.
Percy Jackson has Luke Castellan, who looks after Percy when he first arrives in Camp Half-Blood in The Lightning Thief, and even gives him some cool magic items to help in on his very first quest. It's just a shame that the items are cursed to drag Percy down to Tartarus, and that Luke's the titular Lightning Thief, Big Bad Kronos' Dragon, and one of the main villains of the series.
Trapped On Draconica: Daniar is this for Erowin; taught her martial arts and tries to keep her away from bad habits like drinking during the day. She's too heavy on the 'stern' and not enough on the 'buddy' for Erowin's tastes.
Simon Tam to River in Firefly. He is kind of a doting big brother but he also has to extend that role far beyond what that would normally imply due to the extreme situation. And he never punches her.
In Highlander: The Series, Methos falls somewhere between this and a Trickster Mentor to Duncan. The only problem is that Methos has spent hundreds of years avoiding fights and thus is disinclined towards beating a lesson into the overly stubborn and idealistic Duncan, and thus he often has to hope that his points get through Duncan's thick skull on their own merits.
Duncan was this to Richie before and after the latter became Immortal.
Kamen Rider Decade - Kaitou, the series' rival Rider, became one of these to Asumu when the cast visited an alternate version of Kamen Rider Hibiki. It crosses over with Morality Pet, since up until then Kaitou had been more interested in acquiring treasure than fighting villains, and only helped out the good guys when he felt he owed them or that there was something in it for him.
Riku also shows examples of this trope to the hero Sora throughout all of the games.
Chris Redfield to Claire Redfield, literally, in Resident Evil. Or so it's been implied.
Rei is a roguish variant on this to Ryu and Teepo in Breath of Fire 3, teaching them how to mug people and hunt efficiently. Though he appears to die when Balio and Sunder torch the heroes home, allowing Ryu to begin his adventure, he returns after the Time Skip as an Anti-HeroLancer to the (now more well-rounded and heroic) Ryu.
Sasuke from Sengoku Basara acts like this toward his young master Yukimura, being his friend and advisor and protecting him in dangerous situations. He also acts as emotional support and makes sure he toes the line.
Guy is this to Luke in Tales Of The Abyss. He in his own words, "raised [Luke] from a blank slate to a spoiled, selfish kid" and continues to watch out for and offer him advice throughout the game. At one point, he actually DOES punch Luke when Luke says that he will die in Asch's place at the Tower of Rem, and the punch is hard enough to knock Luke flat on the floor.
Occasionally the line gets blurred between whether Guy is an older brother or surrogate guardian to Luke, given both the little attention and affection Luke's own father, the Duke initially shows towards him, as well as Guy assuming responsibility for shortcomings in Luke's character. Usually this is negligible as Van is a more obvious surrogate guardian.
Persona 4 can see the Protagonist acting this way toward Shu, Kanji, and Naoki. The latter two are actually his underclassmen.
In Fuuin no Tsurugi, Klein saw both Dieck and the dead Prince Mildain as such. In both cases, Klein's supports can potentially have him find his missing "brothers" serving in Roy's army: Dieck left to not cause the Reglay House trouble, while Mildain took the identity of Elphin to evade the noblemen who wanted him dead.
Shu from Arc The Lad functions as this for Elc in the beginning of the second game. Elc handles most things alone, but when he winds up in a jam, he knows where to go for advice and backup.
Kyousuke from Little Busters could almost define this: he's only a year older than the other characters, but he has the sense of competence, charisma, and confidence that makes all of the other Little Busters look up to him. Riki even says early on that he has the air of an older brother and that everyone always listens to what he says. And since what he says normally involves bringing everyone along on wild, fun adventures, they're more than happy to. But if he honestly thinks hurting one of them in the short-term will be better for them in the long run, he will definitely do it. Reluctantly, but surely.
Huey, the main character of The Boondocks is an example to his younger brother Riley (and possibly to his Grandfather as well). Considering though that Riley is quite the arrogant Jerk Ass, Huey ends up "educating him the hard way" more often than most Big Brother Mentors.
As with the comics example, Nightwing to Robin (Tim Drake) in the second season.
Superman eventually becomes this to Superboy (but it takes a Hell of a long time for it to happen and when it finally does it's off camera via a time skip).
The Voltron Force, especially Lance, serve as Big Brother/Big Sister mentors to the cadets in Voltron Force
In ThunderCats (2011), Tygra acts as an interesting combination of this and the The Rival to Lion-O. While he makes no effort to hide how resentful he is of Lion-O's status as The Chosen One, he's also shown that he'll always have Lion-O's back when he's in trouble and has even given him some support when Lion-O doubted himself.