(1) The yielding of a point or privilege, often unwillingly. (2) An acknowledgement or admission.
When the company agreed to pay millions of dollars in damage claims, the payments were seen as a concession that somebody had done something wrong.
When the baseball strike of the 1980s was settled, both players and management had to make concessions. This meant that each side conceded (gave up or reduced) some of its demands until they reached agreement. Concede can also mean simply "admit." So your boss may concede that she is at fault for something, or you may have to concede that your opponent in an argument has some good points.