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Checkmate
Your king is never "captured" or taken off the board. It can be threatened if an enemy piece gets to a position where its next move would land it on the square your king occupies. This is called "check." You may be able to escape check by capturing the attacker, blocking its path with another piece, or moving your king to a vacant square. If you cannot escape, the situation is "checkmate" and you lose.
Other Ways to Win
Checkmate is not the only way to win or lose a game of chess. In timed games, you win if your opponent's time runs out and you still have seconds on the clock to spare. Players who conclude they have no chance of winning may also resign. Traditionally, the player who resigns lays down his king.
Stalemate
A stalemate occurs where a king is not in check, but would be if it moved into any neighboring square. Stalemated players must have no other piece they could move instead of the king. In this situation, the game cannot continue and ends in a draw. Stalemate also happens when the only pieces left on the board are the two kings.
Other Ways to Draw
Players can agree to draw a game at any time. Also, if one king is alone on the board, and the other player has just one knight or bishop left, this counts as a draw. You can claim a draw if your opponent repeats the same move three times, or the game is played against the clock and you both run out of time. It's also a draw if 50 moves are made without anyone moving a pawn or capturing a piece.
Chess Points
Sometimes, you may wish to try for a draw rather than press for a win. In tournaments where you play several games, a win is worth one point and a draw half a point. If your opponent is in a commanding position, playing for a draw may expose you to less risk and bolster your score for the tournament.