Costumes are pieces of equipment that are completly cosmetical in their nature. They do not provide any benefits otherwise. They can be equipped in a characters costume equipment window. When equipped, their sprite will be displayed instead of any non-costume equipped in the same slot.
You can exchange your equipment plus a specific amount of zeny for its costume variant at Costume Exchanger in Geffen (geffen, 178|127).
Currently only those items listed below have a costume variant.