"downy, having an abundance of nap on the surface," c. 1500, noppi, from nap (n.1) + -y (2). Earlier, of ale, "having a head, foamy" (mid-15c.), hence, in slang, "slightly intoxicated" (1721). Meaning "fuzzy, kinky," especially used in colloquial or derogatory reference to the hair of black people, is by 1840. It also was used of sheep. Related: Nappiness.
British colloquial for "baby's diaper," 1927, from use of napkin in this sense. Related: Nappies.