Much like a Foil character mimics tinfoil used by jewelers to emphasize the shine of a gemstone with their differences, a Mirror Character reflects a character's traits to highlight the similarities.
Mirror Characters, also known as Parallel Characters in some literary circles, almost certainly share personality traits, values, similar skill sets, and possibly even goals and likely a narrative arc. They may have the same or similar background, whether they're from the Wrong Side of the Tracks or born a Royal Brat. They might have have shared the same mentor in the past (or even the present). If they have none of the same backstory at all, their similarities will be significant for coming about regardless of their environment.
Think of them like the character versions of Bookends: the similarities serve to highlight something important about the characters and their story.
Typically, Mirrors will be antagonists of some sort, especially an Arch-Enemy. They are almost certainly The Rival, as two characters reflecting each other so strongly on the same side is often jarring. They can be a Sidekick, but as these characters are generally equals, a successor is more likely.
While a Mirror is seen as the literary opposite of a Foil, in truth the tropes often overlap and a character's Foil and Mirror can be the same character. Call them Mirror Foils, and both the Evil Counterpart and Shadow Archetype are often used to create one.
See "Not So Different" Remark for examples where the Mirror relationship is lampshaded in-universe. Contrast Expy for suspiciously similar characters existing in different works in a way that's clearly intended to be a homage—Mirrors have to be in the same narrative. For plot lines that reflect each other, see Plot Parallel. Compare Counterpart Artifacts, which are mirroring objects.
Please note that Mirror Characters have to be characters. Characters who are very similar to a group they don't belong to is not this trope. For two groups that mirror each other, see Mirroring Factions.
Not to be confused with Mirror Match, Left-Handed Mirror, or Mirror Self.
Tropes common with Mirror Characters
Alternate Self: A character's counterpart in an alternate reality to their own.
Arch-Enemy
Back-to-Back Badasses
Balance Between Good and Evil
Bash Brothers
Beat Them at Their Own Game
Birds of a Feather
Blood Brothers
Changing of the Guard
Commonality Connection: Two characters start to get along after learning they have something in common.
Counterpart Artifacts
Doppelgänger
Doppelgänger Dating
Doppelgänger Replacement Love Interest
Dueling Messiahs
Evil Counterpart: A villain who is essentially an evil version or polar opposite to the hero.
Evil Former Friend: The villain used to be the hero's friend.
Evil Knockoff: An artificial being (such as a clone or a robot) created to be an evil version of the hero.
Evil Twin
Fallen Hero
Fearful Symmetry
Friendly Enemy
Future Foil
Generation Xerox
Hero's Evil Predecessor
History Repeats
The Horseshoe Effect
I Resemble That Remark!: Someone objects to an insult in a way that only proves the accusation is true.
Junior Counterpart
Left-Handed Mirror
Like Cannot Cut Like
Mentor's New Hope
Mirror Boss: A video game boss who has the same abilities as the player character.
Mirror Match
Mutual Disadvantage
Only I Can Kill Him
The Only One Allowed to Defeat You: The villain doesn't want anyone else to defeat the hero they're opposed to.
The Only One I Trust
Other Me Annoys Me: A character is irritated by a different version of themselves.
The Rival
Rival Turned Evil
Shadow Archetype
Similar Squad
Stock Shōnen Rival
Sympathetic P.O.V.
Sympathy for the Devil
Sympathy for the Hero:
Take Up My Sword
Too Much Alike: When people can't get along because of how similar they are.
Undead Counterpart
Worthy Opponent
Yearning for a Nemesis