1630s, "to make a concession of, yield up" (transitive), from Middle French concéder or directly from Latin concedere "give way, yield, go away, depart, retire," figuratively "agree, consent, give precedence," from con-, here probably an intensive prefix (see con-), + cedere "to go, grant, give way" (from PIE root *ked- "to go, yield").
From 1640s as "to admit as true." Intransitive sense "accept a disputed point, yield" is from 1780; especially "admit defeat" in an election (1824). Related: Conceded; conceding.