If you concede something, you admit that it is true, proper, or certain — usually in an unwilling way and often in the context of a competition, as in "At midnight, the candidate finally conceded defeat."
In its most common senses, a near synonym of concede is acknowledge — if your mom is pointing out that you need sleep before the test, you should concede the truth of what she's saying. But another meaning of concede is to give away or grant something, as when an unpopular leader is unwilling to concede power. Concede is from Latin concēdere, from the prefix com-, "completely," plus cēdere, "to go along, grant, yield." The corresponding noun is concession.