late 14c., "give up, surrender, abandon, submit; relinquish," from Old French resigner "renounce, relinquish" (13c.), from Latin resignare "to check off, annul, cancel, give back, give up," from re- "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 sense 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 of "give up a position" is first recorded late 14c. Sense of "to give (oneself) up to some emotion or situation" is from 1718. Related: Resigned; resigning.