AP Potion is an item of consumption.
This item regenerates Full AP , it can be used when your AP isn't at his limit. If you use this potion whereas your AP is close to your limit of AP, your AP will surpass the limit restrained by your level.
It can be obtained by completing quests in Event. It can be also a reward for Login Bonus and Missions.
It's recommended to buy the packs containing tickets in the Magia Stone Shop, and when starting out the packs containing only potions are also worthwhile.