Check
The king is the whole game. Capturing the king, whether by accident or design, would end the game, perhaps prematurely. So the people who developed chess came up with a little insurance to make sure the game wouldn't end accidentally. Every time the king is threatened with capture, he is warned. This gives him a fighting chance to escape the fate of the other pieces and pawns. This warning is referred to as check.
The Black king on g8 is in check from the White bishop on c4.
The White king on g1 is in check from the Black rook on g8.
The White king on e1 is in check from the Black knight on d3.
The Black king on d5 is in check from the White pawn on e4.
The White king on a1 is in check from the Black queen on e5 along the a1-h8 diagonal.
A check is a situation where the king would be in danger of being captured if that were allowed. Instead, the player whose king is in check must drop everything and find a way to get out of check. Any piece or pawn is subject to a similar situation, but no warning is required and the player can ignore the threat to his piece or pawn if he wishes or if he is inattentive.
It sometimes happens that neither player noticed a check for several moves. When this is discovered, the players are required to retrace the moves until the king was first in check. It also sometimes happens (in the games of very inexperienced players) that both kings are in check. Such a situation is of course not allowed and the moves must be retraced to a point where only one king is in check.
Three Ways Out of Check
When your king is in check, you must find a way out. There are only three possible ways to get out of check. They are:
Capture the attacker.
Move the king.
Block the attack.
The first way is often the best way. By capturing the piece or pawn delivering the check you not only get out of check so the game can continue, you also remove something valuable to your opponent from the board. Killing two birds with one stone is always good strategy in a game you are trying to win.
The Black king on e8 is in check from the White queen on h5. Get out of check by capturing the queen with the knight on f6.
Black has successfully gotten out of check, picking up a queen in the process.
The second way is the first thing inexperienced players think of, often the only thing. The king is in danger? Move him out of the way. But you must be careful to move the king to a safe square.
The Black king on e8 is in check from the White queen on h5. Move the king to the safe square f8.
Black has successfully gotten out of check by moving the king to a safe square.
The third way only works when your king is in check from a long-range piece with some squares in between the king and the attacking piece. You can block such a check by moving a friendly piece or pawn in the way of the attacker, thus cutting off its long-range power.
The Black king on e8 is in check from the White queen on h5. Block the check by moving the g-pawn to g6.
Black has successfully gotten out of check by blocking the dangerous e8-h5 diagonal with the g-pawn. Note that the g-pawn is now ready to capture the queen in the next move.
Saying Check
When you place your opponent's king in check, you can say check if you wish, but this is not required. If your opponent is experienced, she will know that her king is in check and will go about trying to find a way out. The check itself is the warning. It is automatic and inherent in each check. Actually saying “check” is a reminder and that reminder is not required.
If your opponent is not very experienced, he may play a move that does not get his king out of check, thus forcing him to take the illegal move back and make another move that does get him out of check.

