As the game progresses, you'll meet different characters who'll ask you to complete certain quests for them. The quests include searching specific rooms, tracking down certain items, assembling collections, playing mini-games, and much more. After completion of a quest, the character might take a shine to the items and keep them for themselves.
Collections are special sets of 5 items that the player gets for performing different actions in-game, such as searching rooms, interacting with opponents, and playing mini-games. Via the collection window, you can trade in an assembled collection to receive a bonus, shown on a panel below the collection items. Each collection trade-in consumes 1 copy of each of the gathered collection items and the special requisites. You can find the requisites by interacting with characters at different locations or by purchasing them at the store.