Ability Points, or AP for short are a gameplay feature introduced to the main series in Epic Battle Fantasy 3. They are special points earned after each victorious battle used for learning and upgrading character's Skills, which makes them one of crucial means of increasing character's strength and combat versatility.
AP are awarded automatically to all living party members at the end of each won battle, similarly to gold and experience. The amount of points received depends on the type and level of the enemy, with stronger foes yielding more AP. Each character receives the same amount of AP, including the one in backup slot, which prevents a single character to heavily fall behind the rest of the team.
AP are used to teach the character new skills, expanding his/her available moveset, or to upgrade character's skills onto higher level, improving their power and effects. Various skills cost different amount of AP, most of the time the more advanced the skill and the higher level it is upgraded into the more expensive it is.
In EBF4 special skills, which are skills available to multiple characters, but only one person can learn it at the time, can by unlearned at any time, but doing so won't return any Ability Points spent on them.