A chess term. It comes from the German word meaning "compulsion to move". It describes a situation where the unfortunate player is forced to make a move but every possible move only makes his position worse.
The irony is that the best possible move when you are in zugzwang is not to make a move, but the rules declare that the player has to make a move. Forcing your opponent into zugzwang is an elegant way to force a resignation.
An example of zugzwang:
A H
+----+----+----+----+----+----+----+----+
| | | | | | | | | 8
+----+----+----+----+----+----+----+----+
| | | | | | | | |
+----+----+----+----+----+----+----+----+
| | | | | | | | |
+----+----+----+----+----+----+----+----+
| | | wK | bp | | | | |
+----+----+----+----+----+----+----+----+
| | | | wP | bk | | | |
+----+----+----+----+----+----+----+----+
| | | | | | | | |
+----+----+----+----+----+----+----+----+
| | | | | | | | |
+----+----+----+----+----+----+----+----+
| | | | | | | | | 1
+----+----+----+----+----+----+----+----+
wK - white King
wP - white pawn
bk - black King
bp - black pawn
Whoever has to move will lose because they will have to move their king, leaving their pawn open to capture and eventually to promotion of their opponent's remaining pawn.
Also a great word to play in Scrabble, as you might get to play all seven tiles and get the 50 point bonus. The downside is it needs a blank tile for the extra "Z".