Old English etan (class V strong verb; past tense æt, past participle eten) "to eat, devour, consume," from Proto-Germanic *etanan (cf. Old Frisian ita, Old Saxon etan, Middle Dutch eten, Dutch eten, Old High German ezzan, German essen, Old Norse eta, Gothic itan), from PIE root *ed- "to eat" (see edible).
Transferred sense of "slow, gradual corrosion or destruction" is from 1550s. Meaning "to preoccupy, engross" (as in what's eating you?) first recorded 1893. Slang sexual sense of "do cunnilingus on" is first recorded 1927. Eat out "dine away from home" is from 1933. The slang phrase to eat one's words is from 1570s; to eat one's heart out is from 1590s; for eat one's hat, see hat.