late 14c., "to give up, surrender (oneself or something), give over utterly; to yield (oneself) utterly (to religion, fornication, etc.)," from Old French abandoner (12c.), from adverbial phrase à bandon "at will, at discretion," from à "at, to" (see ad-) + bandon "power, jurisdiction," from Latin bannum, "proclamation," from a Frankish word related to ban (v.).
Etymologically, the word carries a sense of "put someone under someone else's control." Meaning "to give up absolutely" is from late 14c. Related: Abandoned; abandoning.