Checkmate is a term in the game of chess, derived from the Persian Shah Mata, or, The king is dead, which has passed into common parlance as the final, decisive outcome of a battle or head-to-head contest of some kind. Webster 1913 describes this usage as meaning "Utter defeat or overthrow". It is often abbreviated to 'mate'.

In chess, checkmate is defined as a check, or attack on the king, from which there is no escape. There are three possible ways to escape a check:

  1. Capture the piece giving check
  2. Interpose a piece between the king and the piece giving check
  3. Move the king out of check
If none of these options is available, for whatever reason, then it is checkmate and the game is over.

The best way to begin learning chess, after learning how the different pieces move, is to begin to learn the basic positions in which checkmate can be given by each piece, and then by combinations of pieces. There are also traditional forms of chess problem composition which take the form "White (or Black) to move and give checkmate in x moves", with the most popular being 2 and 3 moves. 1-move problems are too simple (any decent chess player should spot a 1-move checkmate immediately, no matter how complicated).

There are also several special or common forms of checkmate which have their own name (note: stalemate is not included here, since it is not a form of checkmate). These include:

Checkmate is also the name of a ballet involving a game of chess between Love and Death, choreographed by Ninette de Valois, with music by Sir Arthur Bliss, first produced in Paris, in 1937. (Thanks to Gritchka for this)

So much for the serious stuff. A quick seach on Google reveals that the word checkmate is used by various companies and websites offering services ranging from the conventional to the bizarre:

Finally: Checkmate is also a kind of move in a square dance.