A chess puzzle is based on a position which could occur in a real game. In fact, most puzzles are taken from games played in competition between expert opponents. Either White or Black may be on the move. The puzzle solver is asked to find the continuation which checkmates the fastest, which wins the most material, or which draws despite a hopeless material disadvantage.
Puzzles usually illustrate a tactical theme. Most players believe that solving puzzles is a good way to improve the ability to calculate variations and to recognize the many tactical opportunities that can occur in a chess game.
Another type of chess puzzle, like the Knight's Tour or the Eight Queens Problem, is based on mathematical curiosities related to the legal moves of the pieces. They have nothing to do with the conduct of a game and the Kings are often missing from the board.
