c. 1200, "nun's head covering," from Anglo-French and Old North French veil (12c., Modern French voile) "a head-covering," also "a sail, a curtain," from Latin vela, plural of velum "sail, curtain, covering," from PIE root *weg- (1) "to weave a web." Vela was mistaken in Vulgar Latin for a feminine singular noun. To take the veil "become a nun" is attested from early 14c.
late 14c., from Old French veler, voiller (12c.), from Latin velare "to cover, veil," from velum "a cloth, covering, curtain, veil," literally "a sail" (see veil (n.)). Figurative sense of "to conceal, mask, disguise" (something immaterial) is recorded from 1530s. Related: Veiled; veiling.