A coif ('kwaff') is a close fitting cap of medieval origins worn by both men and women that covers the top, back, and sides of the head. Sometimes had long, dangling fabric called lappets. If it's not close-fitting, it's likely to be a headscarf or a veil instead. If it covers the cheeks and neck, it's a wimple instead. A white coif is usually a part of a traditional nun headdress, worn underneath a black veil.