AP (Ability Points) are points that are used in both Kingdom Hearts, Kingdom Hearts: Chain of Memories, and Kingdom Hearts 2 to equipped the game's characters with abilities. The overall AP can be increased by leveling up, using items such as AP Boost, or wearing equiptment that will increase the overall AP. If the player does not have enough AP, they cannot equipt certain skills until they have more AP or take off other abilities.
In Kingdom Hearts: CoM, AP works differently. By selecting the option to level up your AP, you are giving another ability that you can use to card sleight with. There is no AP in CoM specifically, but only the option to learn the moves as you level up the AP.