Hunger, a factor people wanted in Pokémon games and that has always been in Mystery Dungeon games, also features in these two games;

As your Rescue Force travels around, your Pokémon will start to get hungry. In the menu's a hunger display is shown to show how hungry your Pokémon is
If it's not hungry at all or only slightly hungry, HP can gradually go up while walking around, however if your Pokémon gets really hungry your HP will go down as you walk.

This could force you to go into a harder level of a dungeon to try and get some food if you have eaten all of the food you can find in that floor of the dungeon.

There are several types of food such as Apples so it should be easy to find the food, but it's always best to stock up in the shops.