fig (n.) Look up fig at Dictionary.com
early 13c., from Old French figue (12c.), from Old Provençal figa, from Vulgar Latin *fica, from Latin ficus "fig tree, fig," which, with Greek sykon, Armenian t'uz is "prob. fr. a common Mediterranean source" [Buck], possibly a Semitic one (compare Phoenician pagh "half-ripe fig"). A reborrowing of a word that had been taken directly from Latin as Old English fic.

The insulting sense of the word in Shakespeare, etc. (A fig for ...) is 1570s, in part from fig as "small, valueless thing," but also from Greek and Italian use of their versions of the word as slang for "vulva," apparently because of how a ripe fig looks when split open [Rawson, Weekley]. Giving the fig (French faire la figue, Spanish dar la higa) was an indecent gesture of ancient provenance, made by putting the thumb between two fingers or into the mouth, with the intended effect of the modern gesture of "flipping the bird" (see bird (n.3)). Also compare sycophant. Use of fig leaf in figurative sense of "flimsy disguise" (1550s) is from Gen. iii:7.