A bandage is a piece of tape or cloth that's used to slow the flow of blood from a cut or another wound. Any good first aid kit is equipped with plenty of bandages.
A bandage can vary from being a tiny plastic strip you stick on the spot where your cat scratched you to a thick, wide cloth that's applied to a serious injury at a hospital. You can also use it as a verb: "If I were you, I'd bandage that skinned knee so it doesn't get dirty." Bandage is a Middle French word, from the Old French bander, "to bind," and ultimately bande, "a strip."