coif n.

late 13c., "close-fitting cap," from Old French coife "skull-cap, cap worn under a helmet, headgear" (12c., Modern French coiffe), from Late Latin coifa "a cap, hood" (source of Italian cuffia, Spanish cofia, escofia), of West Germanic origin (compare Old High German kupphia, Middle High German kupfe "cap"). As "light cap of lace worn by women," mid-15c.

mid-15c., coifen, "to cover with a cap," from Old French coifier, from Old French coife (see coif (n.)); sense of "to arrange the hair" is attested in English from 1835. Related: Coifed; coifing.