resign (v.)

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.

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Definitions of resign from WordNet

resign (v.)
leave (a job, post, or position) voluntarily;
The chairman resigned when he was found to have misappropriated funds
Synonyms: vacate / renounce / give up
resign (v.)
give up or retire from a position;
The chairman resigned over the financial scandal
Synonyms: leave office / quit / step down
resign (v.)
part with a possession or right;
resign a claim to the throne
Synonyms: release / relinquish / free / give up
resign (v.)
accept as inevitable;
He resigned himself to his fate
Synonyms: reconcile / submit