An AP Potion is used for extra credit to play certain chapters/stages, say, if you use 3 AP, you'll use 3 AP from your AP limit, AP recovers over time by 1 (every 3 minutes), if you don't have enough AP, you can use an AP potion to recover all AP, and the trophy will unlock.
Note: You'll have 1 AP Potion when you start the game for the 1st time (or can be earned by completing "Missions").