Checkmate

Checkmate (often shortened to mate) is a game position in chess and other chess-like games in which a player's king is in check (threatened with ) and there is no way to avoid the threat. Checkmating the opponent wins the game.
In chess, the king is never captured—the player loses as soon as their king is checkmated. In formal games, it is usually considered good etiquette to an inevitably lost game before being checkmated.
If a player is not in check but has no legal move, then it is "stalemate", and the game immediately ends in a draw. A checkmating move is recorded in algebraic notation using the hash symbol "#", for example: 34.Qg7#. 
Examples.
A checkmate may occur in as few as two moves on one side with all of the pieces still on the board (as in Fool's mate, in the opening phase of the game), in a middlegame position (as in the 1956 game called the Game of the Century between Donald Byrne and Bobby Fischer), or after many moves with as few as three pieces in an endgame position.
Etymology.
The term "checkmate" is, according to the Barnhart Etymological Dictionary, an alteration of the Persian phrase "shāh māt" () which means "the King is helpless". Persian "māt" applies to the king but in Sanskrit "māta", also pronounced "māt", applied to his kingdom "traversed, measured across, and meted out" thoroughly by his opponent; "māta" is the past participle of "mā" verbal root. Others maintain that it means "the King is dead", as chess reached Europe via the Arab world, and Arabic "māta" () means "died" or "is dead". 
Moghadam traced the etymology of the word "mate". It comes from a Persian verb "mandan" (), meaning "to remain", which is cognate with the Latin word and the Greek "menō" (, which means "I remain"). It means "remained" in the sense of "abandoned" and the formal translation is "surprised", in the military sense of "ambushed". "Shāh" () is the Persian word for the monarch. Players would announce "Shāh" when the king was in check. "Māt" () is a Persian adjective for "at a loss", "helpless", or "defeated". So the king is in "mate" when he is ambushed, at a loss, helpless, defeated, or abandoned to his fate.
In modern Persian, the word 'mate' depicts a person who is frozen, open-mouthed, staring, confused and unresponsive. The words "stupefied" or "stunned" bear close correlation. So a possible alternative would be to interpret "mate" as "unable to respond". A king is "mate" (shah-mat) then means a king is unable to respond, which would correspond to there being no response that a player's king can make to their opponent's final move. This interpretation is much closer to the original intent of the game being not to kill a king but to leave him with no viable response other than surrender, which better matches the origin story detailed in the Shahnameh.
In modern parlance, the term "checkmate" is a metaphor for an irrefutable and strategic victory.
History.
In early Sanskrit chess ( 500–700), the king could be and this ended the game. The Persians (c. 700–800) introduced the idea of warning that the king was under attack (announcing "check" in modern terminology). This was done to avoid the early and accidental end of a game. Later the Persians added the additional rule that a king could not be moved into check or left in check. As a result, the king could not be captured, and checkmate was the only decisive way of ending a game.
Before about 1600, the game could also be won by capturing all of the opponent's pieces, leaving just a bare king. This style of play is now called "annihilation" or "robado". In Medieval times, players began to consider it nobler to win by checkmate, so annihilation became a half-win for a while, until it was abandoned.
Two major pieces.
Two (queens or rooks) can easily checkmate on the edge of the board using a technique known as the ladder checkmate. The process is to put the two pieces on adjacent or and force the king to the side of the board by using one piece to check the king and the other to cut it off from going up the board. In the illustration, White checkmates by forcing the Black king to the edge, one row at a time. The ladder checkmate can be used to checkmate with two rooks, two queens, or a rook and a queen.
Basic checkmates.
There are four fundamental checkmates when one side has only his king and the other side has only the minimum needed to force checkmate, i.e. (1) one queen, (2) one rook, (3) two bishops on opposite-colored squares, or (4) a bishop and a knight. The king must help in accomplishing all of these checkmates. If the superior side has more material, checkmates are easier.
The checkmate with the queen is the most common, and easiest to achieve. It often occurs after a pawn has queened. A checkmate with the rook is also common, but a checkmate with two bishops or with a bishop and knight occurs infrequently. The two-bishop checkmate is fairly easy to accomplish, but the bishop and knight checkmate is difficult and requires precision.
King and queen.
The first two diagrams show representatives of the basic checkmate positions with a queen, which can occur on any edge of the board. Naturally, the exact position can vary from the diagram.
In the first of the checkmate positions, the queen is directly in front of the opposing king and the white king is protecting its queen. In the second checkmate position, the kings are in opposition and the queen mates on the (or ) of the king.