To concede can mean multiple things. In golf, it typically means only one thing, particularly as it pertains to match and "skins" play. Fortunately, the definition of conceding a hole in golf is quite simple to comprehend.
The Merriam-Webster Dictionary defines to concede as "to grant as a right or privilege," or, "to acknowledge grudgingly or hesitantly."
In golf, the definition is almost a blend of those from the dictionary. Essentially, in competition--whether friendly or otherwise--conceding a hole means stopping play on a hole and admitting that another player has "won" the hole.
Conceding a hole in golf helps speed up the game. Once a player realizes he has little or no chance of winning a hole in match or "skins" play, he has the opportunity to stop play and acknowledge as much. For instance, if one player is on the green in three shots, while another has hit four shots but is in the woods, the latter player may simply concede the hole, realizing there's almost no chance of halving or winning the hole. In order to keep the game moving, this player might concede, award the hole to the other player and move on to the next tee.
Hole concessions are most typically found in match or "skins" play. The former features players competing against one another, attempting to win more holes over the course of 18 holes than their opponents. In "skins" play, meanwhile, a group of players (typically four) squares off in the hopes of winning holes, or "skins," with the victor recording the most skins. In both forms of play, once a player realizes he or she has no shot of winning a hole, rather than play it out, they concede the hole in order to expedite play.
Another common concession in golf is to concede short putts. In casual foursomes, short putts are often conceded out of courtesy and to expedite play, whether the outcome of a match could be affected or not. But short putts are often conceded in professional play, too. A story in a 1957 Sports Illustrated tackled the very topic of whether golfers should or should not concede putts. PGA Tour pros and executives were polled, with the consensus being that, in match play, players were better served by not conceding putts.