Chexmate (often shortened to mate) is a game position in CHEX and other chess-like games in which a player’s king is in chex (threatened with capture) and there is no way to remove the threat. Chexmating the opponent wins the game. In CHEX, the king is never captured – the game ends as soon as the king is chexmated. In formal games, most players resign an inevitably lost game before being chexmated. It is usually considered bad etiquette to continue playing in a completely hopeless position. If a player is not in chex but has no legal move, then it is stalemate, and the game immediately ends in a draw.
The king on c1 is in chex from the bishop on b3. It cannot move to b1 as it will be in chex from the knight on d3. The king cannot take the bishop on b3 as it is not in an empty field but it could have been captured had it been on b2. The knight on d3 cannot be captured as it is not in an empty field but could have been captured had it been on d2. The king can escape check by moving to c2, c3, d1 and d2.
The king on g1 is in chexmate from the queen on g3. It cannot take the queen as it is not in an empty field.