muff

Etymology 1

Probably from Dutch mof (“muff, mitten”).

noun

1. (historical) A piece of fur or cloth, usually with open ends, used for keeping the hands warm.
2. (vulgar, slang) Female pubic hair; female genitals (vulva, vagina), like muffin. See Thesaurus:vagina.
3. (by extension, vulgar, slang) A woman or girl.
4. (glassblowing) A blown cylinder of glass which is afterward flattened out to make a sheet.
5. The feathers sticking out from both sides of the face under the beak of some birds.
6. A short hollow cylinder surrounding an object such as a pipe.

Etymology 2

Unknown; perhaps a specialised use of Etymology 1, above; or perhaps related to Dutch muffen (“to dote”) and German muffen (“to sulk”).

noun

1. (colloquial) A fool, a stupid or poor-spirited person.
   Can you fancy that such an old creature (an old muff, as you call him, you wicked, satirical man!) could ever make en impression on my heart? 1860, William Makepeace Thackeray, Lovel the Widower
2. (slang, chiefly sports) An error, a mistake; a failure to hold a ball when once in the hands.
3. A bird, the whitethroat.

verb

1. (sports) To drop or mishandle (the ball, a catch etc.); to play badly.
2. To mishandle; to bungle.
   Here was the superlative opportunity to make a generous and lasting settlement from a position of strength; but the pieds noirs, like the Israelis, and from not altogether dissimilar motives, were to muff it. 1977, Alistair Horne, A Savage War of Peace, New York: Review Books, published 2006, page 69

Etymology 3

Shortening.

noun

1. (slang) A muffin.
   Skinny lattes and a couple of blueberry muffs. 2010, Lindsay G. Arthur, The Litigators, page 63