A Character is an imaginary persona controlled by a specific player. This might be the Games Master, or any of the other players in the game. This player is responsible for the voluntary actions of the character. For instance the player can decide whether the character will attempt to open a door or not, whether that attempt succeeds is up to the games master.
In most games a character is defined by a set of statistics, numerical representations of physical and mental abilities. Thus a character might have a statistic for Physical Strength, or a numerical rating of their skill with firearms. These statistics are used by the set of rules in the system to determine whether or not some action undertaken by the character succeeds.