Recover your HP by picking up red potions dropped by enemies or buy them from the shops in the middle or at the end of a map. Sometimes, your HP can also be restored by random effect scrolls dropped by mini-bosses or those purchased from the shop. You can increase the amount of HP/MP recovered by spending Desserts on the corresponding upgrades.
MP is required to activate Ultimate Spells. You can recover your MP naturally by collecting Desserts. You can also pick up blue potions dropped by enemies or purchased from the shop to recover a huge amount of MP.
HP and MP potions are rare drops from enemies. Sometimes you’ll get more than you need, sometimes, you’ll be in desperate need of it. To maximize its use for multiple drops, don’t pick up a potion immediately until you clear an area or when you really need it.