Checkmate
If the king is in check and cannot get out of check this is called checkmate and the player who has checkmated his opponent has won the game.
In diagram 1 black is checkmated. His king is in check from the white queen and he cannot get out of check. If he moved to d8 or f8 he would still he in check by the queen. If he moved to d7 or f7 he would be in check from both the queen and the king. If he captured the queen with his king he would be in check from the white king. White has won the game. In diagram 2 black's king is in check from the knight. He cannot move his king to d8 or f8 because he would be in check from the pawn. He cannot move to d7 or f7 because he would be in check from the king. He cannot capture the pawn because he would be in check from the king.
Diagram 1Diagram 1 Diagram 2Diagram 2
In diagram 3 white is in check from the black rook. If he moved to d8 or e8 he would still be in check from the rook. He cannot move to d7,e7 or f7 because he would be in check from the black king. Kings are not allowed to occupy squares next to each other  because they would be in check from one another. In digram 4 the white king is in check from the black rook on a8. If he moved his king to d7,e7 or f7 he would be in check from the other rook.
Diagram 3Diagram 3 Diagram 4Diagram 4
In diagram 5 the black king is in check from the white knight which can jump over the black pieces. The king cannot move because black's own pieces are in the way. The knight cannot be captured. White is checkmate
Diagram 5
Diagram 5
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