In Chess, if the player on turn is in check and cannot make a valid move, is called to be in checkmate. In this case the game ends, the checkmated player loses, and the opponent (the checkmater) wins.
Black is checkmated. The king cannot move and can neither capture the queen as it is defended by the white king.
Fool's mate, two moves after beginning.
White is checkmated. The bishop cannot block the path of the queen as then it would expose the king to check from the rook.
Checkmate in the center.
Smothered mate: the king is blocked by its own pieces.
Not a checkmate yet, because the bishop can be intervened, but after capturing it, the position is a back-rank mate. The king's escape fields are blocked by its own pawns.
There are three possible ways to escape from check (see the check-rule), so checkmate occurs when none of these three is possible:
When giving checkmate, be careful to avoid stalemate: it occurs when a player cannot make a valid move, but is not in check. In such cases, the game ends in a draw. For example:
White's turn: stalemate, because no valid move is possible, but the king is not in check.