late 14c., "give up (something), surrender, abandon, submit; relinquish (an office, position, right, claim)," from Old French resigner "renounce, relinquish" (13c.), from Latin resignare "to check off, annul, cancel, give back, give up," from re-, here perhaps denoting "opposite" (see re-), + signare "to make an entry in an account book," literally "to mark," from Latin signum "identifying mark, sign" (see sign (n.)).
The notion is of making an entry (signum) "opposite" — on the credit side — balancing the former mark and thus canceling the claim it represents. The specific meaning "give up a position" also is from late 14c. The sense of "to give (oneself) up to some emotion or situation" is from 1718. Related: Resigned; resigning.