Not all characters are important to a story. However, those that aren't are normally not developed that well, while plot relevant characters are. On the other hand, sometimes it can go the other way, and minor, undeveloped characters (or a two dimensional main character) can set the plot in a new direction. This trope takes that to its logical conclusion.
This character has an effect on the plot; however, they're never introduced or named or possibly even shown in the background. This is usually the result of them being a Red Shirt or Unwitting Instigator of Doom in someone's backstory (so what they did or what happened to them is only relevant for how it influenced the character whose backstory they appeared in). However, in the most extreme examples, their existence may only be implied (for example, someone who left their MacGuffin or Emergency Weapon lying around for The Hero to find).
Note that while this character might be revealed and fleshed out later, there isn't usually any mystery about who they were; their role is fulfilled just fine by them being just another face in the crowd and they need not have any further effect on the story. The best way to identify a character as this trope is if they can only be referred to by their contribution to the plot and in the past tense, making it clear that they're little more than the reason something happened (e.g. "That guy who gave Bob his sword" or "That urchin who stole Alice's wallet when she was buying her dead sister's medicine"). Indeed, the only reason they exist is the fact that they did something that had to be done by someone, and in this case that someone was nobody important.
Compare The Ghost, who functions as any other character would (and might even be part of the main cast) but is simply never shown on screen (they can overlap; the main difference is that characters who fall under this trope don't have any characteristics, while the ghost can still be a fully fleshed out character), Posthumous Character for already dead characters who are still important to the plot, and the Featureless Protagonist, who can become this trope in sequels. A Badass Bystander will often become this if they don't appear subsequently and aren't given any characterisation beforehand. If they become a recurring character in later works or adaptations, they will often evolve into He Who Must Not Be Seen or The Ghost as a nod to their earlier characterisation (or lack thereof). Contrast Lower Deck Episode and Day in the Limelight for when less developed characters are fleshed out by the plot. Often overlaps with a Cryptic Background Reference or Diabolus Ex Nihilo (for malicious examples).
Aoi aka "The Laughing Man" reveals that he himself was arguably the second part in the eponymous "Stand Alone Complex" (an event where many people spontaneously start copying something which wasn't there in the first place) and the real "Laughing Man" was an unknown person whose email exposing the micromachines company's coverup was found by Aoi.
In the episode "Embraced by a Disguised Net – CAPTIVATED", a member of an Organ Legging gang accidentally kidnaps the daughter of a politician who was denying their existence. The rest of the gang are never shown, but it turns out the entire episode's plot was orchestrated by a rival who had given her a list of kidnapping targets which included the girl so she'd be branded a traitor.
The second generation of Get Backers. They give Ban and Ginji their name, their car, and their analogy of a retrieval being like a jigsaw puzzle, but the only reason they exist is because the identity of the first generation is a major plot twist and a surprise to the cast.
In the background of Fullmetal Alchemist, the War of Ishvalan Extermination was caused by the Ishvalans uprising against the Amestrian military. It's later explained that they did this because an Amestrian soldier shot and killed an Ishvalan child for no discernible reason, but no one knows who this soldier was and the Amestrian military claim that the Ishvalans made him up as an excuse. Later still, the trope is actually subverted when it's finally revealed that the "soldier" was the disguised homunculus Envy, who deliberately started the war as part of the Big Bad's plan.
Joe Chill, the mugger who murdered Bruce Wayne's parents, sometimes functions as this, particularly if his identity is still a mystery to Batman. In other versions of the story, Bruce eventually finds him and he gets dealt with.
The (usually) unnamed robber who killed Spider-Man's uncle Ben. He's literally responsible for Spidey's entire career, but he's generally only ever referred to as "the robber" or "the burglar."
Whenever the Green Lantern Corps appears in force, the background will be littered with unnamed Lanterns who exist simply to fill out the Corps' numbers and give the artist an opportunity to draw weird aliens (and give the bad guys Lanterns to kill other than the ones with names and speaking parts). Sometimes one will strike a chord with an artist or the readers and appear enough times to get a name, but many will only ever appear in one issue, or even one panel.
Films — Animated
The sorceress in Beauty and the Beast who turns the prince into a beast and lays a curse over his entire castle, thus kick-starting the plot. We're given no explanation for why she does this - was she motivated by a sense of justice in putting the prince through a Secret Test of Character, or was it Disproportionate Retribution at being rejected by him? She's also never seen in person, only depicted in stained glass at the beginning of the film.
Many of the events of The Gods Must Be Crazy happen because a pilot flying over Africa's Kalahari Desert - who is never named, never speaks, and appears for only a few seconds - thoughtlessly tosses an empty Coca-Cola bottle out the window.
In Attack of the Clones, the clone army is said to have been first commissioned by a Jedi Master named Sifo-Dyas, who was reportedly killed around the time the Star Wars prequel trilogy began, but gets no more mentions or development in the movies than that. His story is eventually fleshed out in Star Wars: The Clone Wars, where it's revealed that the Sith killed him and took over the clone production.
The man at the beginning of The Chronicles of Riddick who tries to stand up to the Lord Marshall. He gives a little speech, but has no name or any other lines. He exists mainly to show the audience that the Big Bad can literally rip someone's soul out of their body.
Hoid is a mysterious character who has appeared in almost every one of Brandon Sanderson's books; the only exceptions are the Wheel of Time (since they are not originally his books) and the Alcatraz Series. He is seldom named, but inevitably the cause of something that eventually turns out to be instrumental to resolving the plot, even or especially if a story otherwise has no indication of being in the same universe any of his other books.
King Galbatorix from the Inheritance Cycle doesn't appear until the last book, yet he is a constant presence in the series.
Big Brother from 1984 is technically the Big Bad of the story; however, he's never shown in person and it's left up in the air as to whether he really exists in the first place. The same goes for the leader of The Brotherhood (where it's not even revealed whether the organisation he leads even really exists).
In The Malloreon, there is an unnamed character who stole the Sardion (MacGuffin of the series) and deposited it at its final resting place to be found by the heroes 300 years later, along with his remains.
In Rebecca, the main character is the second wife of the eponymous Rebecca's husband. She's compared unfavorably to Rebecca without ever being told anything about her by his staff. Nothing is revealed abut her as they figure she doesn't need to know, except that she died. In the end the protagonist learns more about Rebecca and gains the respect of the inhabitants by saving them from a fire.
In the film adaptation, the head maid refuses to accept her and stays behind to die in the fire.
In The Bible, Cain had a wife, but her very existence is a notorious theological mystery, since Adam, Eve and the murdered Abel are the only other humans mentioned from creation until that point. Later verses do mention his parents having other kids aside from Seth offering a non-linear answer. Sometimes Cain's wife and the closely related issue of everyone having the same parents are offered as reasons to not read Genesis literally. Wild Mass Guessing can include God whipping her up offscreen for Cain and more. Who's right is best left to other venues. She doesn't even get a name, even though both wives of Cain's great-great-great-grandson Lamech are named.
In Charlie and the Chocolate Factory, Willy Wonka's rival candymakers Prodnose, Ficklegruber, and Slugworth qualify as unknowns. In the Backstory, Driven by Envy, they sabotaged Mr. Wonka's operations by sending in spies disguised as workers to steal his recipes so they could come up with Follow the Leader equivalents. Mr. Wonka, desperate to save his work, sacked his entire workforce in response and became a Reclusive Artist who — somehow — managed to get his factory up and running again without anyone entering or leaving it. The question of how he accomplished this is the key reason why the Golden Ticket contest becomes such Serious Business in the present — the chance to actually meet him, see his operations, and learn the answer is one many people want. The rivals have no other plot importance than their Backstory role and are rarely depicted (even in Flashback) in adaptations, with the key exception of the 1971 film version, in which Adaptation Expansion includes a subplot involving Mr. Slugworth's attempts to ruin him in the present by bribing the Golden Ticket finders to steal one of Mr. Wonka's new inventions.
A later episode of Doctor Who, "Listen", gives this to the Monster of the Week, an entity that the Doctor theorizes is the perfect hider, so much so that nothing at all is known about it. By the end of the episode it is unclear if the creature even exists, or if it exists it had appeared in the episode
Vivienne in Merlin, who is also a Posthumous Character. She is the mother of Morgana and Morgause, was married to Gorlois, and had an affair with Uther. That's literally all we know about her.
One episode of M*A*S*H features a helicopter pilot who risks his own life to fly patients to the unit with a broken fan belt in his chopper's engine. He gets a replacement and leaves again, and no one ever even has a chance to learn his name, much less thank him for his bravery. When the medical staff assemble a time capsule at the end of the episode, Hawkeye suggests including the broken fan belt to commemorate the man's courage.
The Little Red-Haired Girl in Peanuts, Charlie Brown's always offscreen, always silent, always unrequited crush. She was briefly shown and named Heather in one of the animated specials, but this is not canon. A 1990s strip showed her in silhouette, dancing with Snoopy.
Bastion has a couple, the most obvious one being the unknown man who seduced and betrayed Zia, which lead to both her surviving the catastrophe...and to her father setting it off. Another example would also be whoever ended up with The Kid's money, which he'd been sending back to his mother (who was already dead). Forcing him to take another tour of duty as a Mason (although with the loss of his mother he might have done so anyway) and surviving the catastrophe.
The Rat Man in Portal who has scrawled graffiti all over the place (although he might be closer to The Ghost, given that he's essentially interacting with the story still). A comic given out with the game's sequel fleshes out this character.
In the game Singularity, you often come across hidden messages that seem to be addressed to you, specifically. The messages are from someone who seems to know you, and who also seems to have done the same things you're doing; before certain major plot points, the messages will actually give you the heads up before anything's actually evident (i.e. "DON'T TRUST HIM", etc). It's later implied to be a future version of yourself who went back in time to leave the messages.
In Quake IV, the protagonist from Quake II is this (Quake IV being the direct sequel to Quake II). He single-handedly invaded the Strogg homeworld and assassinated their leader, allowing a full-scale human invasion. He is never shown or mentioned by name.
The soldier who fired the arrow which killed Harold Godwinson in the Battle of Hastings (thus changing the course of English history).
That said, nearly everyone involved is this trope due to so much of the events being lost in the mists of time. One historical Epileptic Tree is that the entire arrow-to-the-eye story was invented specifically to overshadow the achievement of the (named) knights who probably killed Harold by hand.
The "person from Porlock" who interrupted Coleridge while he was in the middle of writing "Kubla Khan". By the time he'd managed to get the person to leave, Coleridge had completely forgotten the dream that inspired the poem, leaving it forever unfinished.
The man who fired the "shot heard 'round the world" that kicked off The American Revolution. To this day, no one can even agree on whether he was a colonial militiaman or a British Redcoat.