Old English mete "food, item of food" (paired with drink), from Proto-Germanic *mati (cf. Old Frisian mete, Old Saxon meti, Old Norse matr, Old High German maz, Gothic mats "food," Middle Dutch, Dutch metworst, German Mettwurst "type of sausage"), from PIE *mad-i-, from root *mad- "moist, wet," also with reference to food qualities, (cf. Sanskrit medas- "fat" (n.), Old Irish mat "pig;" see mast (n.2)).
Narrower sense of "flesh used as food" is first attested c.1300; similar sense evolution in French viande "meat," originally "food." Figurative sense of "essential part" is from 1901. Dark meat, white meat popularized 19c., supposedly as euphemisms for leg and breast, but earliest sources use both terms without apparent embarrassment.
First record of meat loaf is from 1876. Meat market "place where one looks for sex partners" is from 1896 (meat in various sexual senses of "penis, vagina, body regarded as a sex object, prostitute" are attested from 1590s); meat wagon "ambulance" is from 1920, American English slang, said to date from World War I (in a literal sense by 1857). Meat-grinder in the figurative sense attested by 1951. Meat-hook in colloquial transferred sense "arm" attested by 1919.