1590s, "covering into which both hands may be thrust to keep them warm," from Dutch mof "a muff," shortened from Middle Dutch moffel "mitten, muff," from French moufle "mitten," from Old French mofle "thick glove, large mitten, handcuffs" (9c.), from Medieval Latin muffula "a muff," a word of unknown origin.
The muff was introduced into France toward the close of the sixteenth century, and soon after into England. It was used by both men and women, and in the seventeenth century was often an essential part of the dress of a man of fashion; but it is now exclusively an article of female apparel. [Century Dictionary]
Meaning "vulva and pubic hair" is from 1690s; muff-diver "one who performs cunnilingus" is from 1935.
"to bungle, perform clumsily or badly," by 1840, said to be from pugilism slang, probably related to muff (n.) "awkward person, simpleton" (1837), which is perhaps from muff (n.) on notion of someone clumsy because his hands are in a muff. Related: Muffed; muffing. The noun meaning "anything done in clumsy or bungling fashion" is by 1871.
early 15c., "to cover or wrap (something) to conceal or protect," perhaps from Old French moufle "thick glove, mitten;" see muff (n.). Compare Old French enmoufle "wrapped up;" Middle French mofler "to stuff." The meaning "wrap something up to deaden sound" is recorded by 1761. Related: Muffled; muffling. Muffled oars have mats or canvas about their shafts to prevent noise from contact with the oarlocks while rowing.
in cookery, 1946, from Italian manicotti, said to mean literally "hand-warmers, muff," from Latin manicae "long sleeves of a tunic, gloves; armlets, gauntlets; handcuffs" (see manacle (n.)).
"ponder, turn over in one's mind," 1873, perhaps from a figurative use of mull (v.) "grind to powder" (which survived into 19c. in dialect), from Middle English mullyn, mollen "grind to powder, soften by pulverizing," also "to fondle or pet" (late 14c.), from Old French moillier and directly from Medieval Latin molliare,mulliare, from Latin molere "to grind," from PIE root *mele- "to crush, grind."
Of uncertain connection to the mull (v.) defined in Webster's (1879) as "to work steadily without accomplishing much," and the earlier identical word in athletics meaning "to botch, muff" (1862). Related: Mulled; mulling.
1530s, "a kind of wrap or scarf for the throat and lower part of the face," agent noun from muffle (v.). Mechanical sense of "any device used to deaden sound" is by 1856; specifically as "automobile exhaust system silencer" it is attested from 1895.
"a small, light, round, spongy cake made with eggs," usually eaten buttered and toasted, 1703, moofin, possibly from Low German muffen, plural of muffe "small cake;" or somehow connected with Old French moflet "soft, tender" (said of bread). The historical distinction of the muffin from the crumpet is not entirely clear and the subject is involved. In American English the word was extended to a sort of cup-shaped bun or cake (often with blueberries, chocolate chips, etc.); hence muffin top "waistline bulge over tight, low jeans" (by 2005), from resemblance to baked muffins from a tin. Muffin-man "street seller of muffins" is attested by 1754.
Why sit we mute, while early Traders throng
To hail the Morning with the Voice of Song?
Why sit we sad, when Lamps so fast decline,
And, but for Fog and Smoke, the Sun would shine?
Hark! the shrill Muffin-Man his Carol plies,
And Milk's melodious Treble rends the Skies,
Spar'd from the Synagogue, the Cloathsman's Throat,
At measur'd Pause, attempers every Note,
And Chairs-to-mend! with all is heard to join
Its long majestic Trill, and Harmony divine.
["The Black Bird and the Bull-Finch," 1777]