late 14c., ultimately from Latin februarius mensis "month of purification," from februare "to purify," from februa "purifications, expiatory rites" (plural of februum "means of purification, expiatory offerings"), which is of uncertain origin, said to be a Sabine word. De Vaan says from Proto-Italic *f(w)esro-, from a PIE word meaning "the smoking" or "the burning" (thus possibly connected with fume (n.)). The sense then could be either purification by smoke or a burnt offering.
The last month of the ancient (pre-450 B.C.E.) Roman calendar, so named in reference to the Roman feast of purification, held on the ides of the month. The Old English name for it was solmonað, which is said to mean "mud month." English first borrowed the Roman name from Old French Feverier, which yielded Middle English Feverer, Feoverel, etc. (c. 1200) before the 14c. respelling to conform to Latin.