Leftovers is an item combo. It is leftovers of food (represented by an apple core) that restore 1/16 of the Pokémon's HP (it is rounded down if the number is odd) each turn that the Pokémon holds it.
It was introduced in Generation II and has appeared in every generation since.
The two Pokémon that hold the item Leftovers are Snorlax and its pre-evolution, Munchlax. In all of the games where Snorlax and Munchlax are catchable, both Pokémon will always hold the item when they are caught.