Ability Points (AP) are points that are used in the Kingdom Hearts series to equip the game's characters with abilities. The overall AP can be increased by leveling up, using items such as AP Boost, or wearing equipment that will increase the overall AP. If the player does not have enough AP, they cannot equip certain skills until they have more AP, or if they choose to remove other abilities.
In this game, you can raise your AP through AP Ups that can be synthesized or found in worlds throughout the series, By leveling up, or by equipping Accessories. AP allows you to equip abilities that can act as helpful tools.
In Kingdom Hearts: Chain of Memories, AP is not used at all in Sora's gameplay, rather, it is replaced with CP (card points). CP dictates how many cards can be used in the equipped deck, including offensive and restorative cards Sora and Riku use, as well as the passive-effect Enemy Cards available.
In Kingdom Hearts Re:Chain of Memories, Sora does gain the abilities High Jump, Glide, and Superglide although these simply remain active for the remainder of the game and have no point requirements of any kind.
In Reverse/Rebirth mode, Riku's deck is fixed for each world so he has no CP. While he does possess an AP stat, it comes in the form of Attack Points. He can only gain one AP until gaining five levels since he last boosted his AP. The higher Riku's AP is, the stronger his attacks are.
In this game the player can use AP Boosts on all characters including Sora, Donald, Goofy, and supporting characters. There are many AP Boosts in this game. AP Boosts can also be synthesized at Moogle shops or found in chests throughout the worlds.
In Kingdom Hearts II Final Mix, AP Boosts can be obtained as much as you like by defeating Demyx and Luxord's data battle.