A cloak is a protective garment worn over other clothing. In reality, it protects the wearer from the weather, but in roguelike games it is typically a form of armor. If it has a sticky curse, in some games this will also prevent you from changing your body armor in addition to your cloak, since the cloak is worn over the body armor.
Wearing a cloak can have some additional benefits such as reduction of damage from liquids (typically acid) or the protection of other equipment from environment hazards such as rust.