Items boxes usually serve as a place for players to store unwanted items, and is often found in survival horror games due to the player character commonly having a limited inventory space. In Resident Evil, the item boxes themselves also have a finite amount of inventory space, but there are so many slots that players will never fill it up completely unless they actively attempt to do so.
Resident Evil item boxes are usually found in Save Rooms -- rooms that exist as a safe haven for the player to recuperate. Items stored in there will then persist throughout all item boxes in the game, allowing for a convenient dumping ground for key items that are currently not necessary, or for any spare ammunition and/or healing items ect. However in the Resident Evil remake, there is an unlockable mode titled 'Real Survivor', which--among other effects--will make it so items stored in a particular item box will then forever stay in that specific item box only. This design was in fact the original idea behind item boxes in Resident Evil, however it was eventually deemed as being too punishing.
Oddly enough Resident Evil Zero does not feature item boxes, as instead players can leave items on the ground, which will then persist there until/if the player decides to pick it up again. Resident Evil: Revelations, while is amongst the more action-orientated Resident Evil games, also features item boxs, though they are used only for storing weapons.
In the Silent Hill series the player character usually has infinite inventory space, however Silent Hill 4: The Room bucked this trend by giving protagonist Henry Townshend a limited inventory. This would then force players to often return to Henry's apartment Room to procure and/or store items in an item box.