Character
You may call it that, but it doesn't have any.
A Character is a person in in a story. Sometimes, people in real life get called "characters;" this is not always a positive statement.
Normally, we passively read (or watch, or listen to) an explanation of what they do and what happens to them, but role-playing games (both the tabletop and video varieties) have the unique feature of allowing a player to determine the actions of one or more characters; we refer to such characters as Player Characters.
The other characters in the game world, those not under player control, are called Non-player characters.
Sometimes, a person or character is described as "having character;" in this sense, character is defined as the qualities that define a person, especially the good qualities -- though to say that a character "has no character" usually means that he or she has no distinguishing qualities whatsoever, good or bad.
Because a player may have more than one PC under his control (in different games, or maybe even in one game), and because a DM will inevitably have lots of NPCs running around, players and DMs often use Character sheets (or stat blocks, if the character is of minimal importance) to keep track of a character's essential characteristics for ease of recollection.