The object of the game is to put the opponent's king in check so securely that escape is impossible. This is called checkmate. When checkmate is accomplished while another opponent remains in the game, the checkmated king is removed from the chess board and the checkmated player's pieces are conscipted into the service of the player that accomplished the checkmate. (See below.) The full credit for the checkmate goes to the checkmating player and is not shared.
When a player checkmates the opponent to their right, the opponent to their left gets the next turn and might be able to interfere. This condition is called checkmate pending.