A character point is used to purchase abilities for a character. Your supply of character points is like a budget for purchasing the traits you want. Character points are characteristic of point-based character creation, but also appear in games where a separate pool of points is used to purchase advantages.
In some games, they are equivalent to experience points. In cases where they are not, they may have different costs for abilities than experience points, or they may be used at character creation and never again.
In some games, they serve a secondary function as luck points or hero points.