Pick Up is an ability known by various animals.
In Battle Use
This ability does not play a role in battle.
Out of Battle Use
An animal with the Pick Up ability has the chance of picking up a random item when its wandering around the field. A picked up item shows up after battle. The level of the animal determines the rarity of items that are picked up.
Animals gathering food may have inspired this ability as animals commonly pick up berries as a part of this ability.