Definition: A conceded putt is one that your opponent has told you that you don't have to putt out; he has conceded that you will make the putt.
Let's say you have a 2-footer for par. If your opponent thinks there is no chance you'll miss, he might conceded the putt, telling you to pick it up. Your score is par, same as if you had actually putted the ball into the cup.
Very important: Conceded putts are legal only in match play. They are illegal in stroke play. And conceded putts are solely at the discretion of your opponent (or at your discretion on his putts). They should only be offered, not requested.
