Zugzwang describes a situation in which the obligation to make a move in one's turn is a serious, often decisive, disadvantage. This word comes from the German meaning "compulsion to move" and it's just that - it's your move and you have to move. Whether you want to or not. You have no choice. You cannot skip your turn. It has application in other games, but it is commonly associated with Chess. In the chess world, particularly in a close endgame, it can mean having to give up a chance to win and to have to accept a draw, or it can mean having to give up a draw and having to accept a loss. Any who "push wood" on a regular basis know the in's and out's of the application of this term well. Wikipedia has a article posted, and a link is provided.
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A zugzwang in chess is a type of position. It is a position where the player to move is not in any real danger, but any move he makes would harm his position. It can be thought of as a position where the player's best move would be to pass. The term zugzwang means literally "compelled to move."