As you go through the games, you shall encounter many small chests in the areas. These chests contain Collection items and they respawn when you re-enter the area. Most of these Collection Items are used for trading with other Pokémon in order to receive other items. If you collect all 32 items, you will achieve an achievement with Kecleon

In addition to the small chests, many of the items are received from various Pokémon while others are located within one of the large chests found through PokéPark