A secret character (also “hidden” or “unlockable” character, depending on speaker and context) is a kind of character that you can use by meeting specific conditions.
On occasion, there will be a joke that such-and-such a (very good) player will play ridiculously well (especially with a low-tier character), and that character will be called a secret character (“because obviously the normal version isn’t that good”).
Usually, you have to meet one or more of the following conditions in order to make a character selectable:
Input a particular command sequence at the title screen or character selection screen.
When someone has cleared the game, the character will be unlocked on that system ever afterwards. There are sometimes requirements for how to beat the game, such as which boss you have to beat.
After so many hours or days or months of being in operation, characters become usable. Originally from Tekken 2.
Something like a semi-permanent alternative to an input code, you may be able to enter something at some sort of test screen in a game’s settings in order to unlock a character.
Since this requires access to the settings, you either have to be an operator, or otherwise have the permission of those who host the game on its premises.
By playing the game, you acquire some sort of points, and may spend them on things including but not limited to newly-usable characters. This has been common in games for the Atomiswave.
By using some sort of “cheat device”, or perhaps by modifying the game code (the latter of which I must warn you may be technically illegal, if not just legally dubious in your country), you can often use characters that the developers have allowed no intentional avenue for unlocking. This tends to be a bit buggy, and there are not very many opportunities to do this other than to play as a boss, so there isn’t much of a legitimate purpose for doing this as far as gameplay goes.
Occasionally, you may have to clear minigames, or have unlocked things in a different game. This only shows up in home ports, for the most part.