A bag is the common term for any container that a character uses to hold other items. Bags can be placed in the storage slots at the right-most end of the interface bar. Bags inside bags must be empty. You can purchase extra bag slots for your bank account at gradually increasing rates, starting at 10 for the first slot.
Normal bags can hold any sort of item, unlike special bags that can only hold specific types of items. Special bags give the player more slots to store items, with the exchange of only being able to put certain types of items in them. Specials bags are generally cheaper than normal bags of the same size.