In the chess endgame of King and Rook vs King, one player has a Rook and a King, while the other player has only a King. The objective for the player with the Rook is to checkmate the opposing King, which means putting it in a position where it cannot escape capture. To achieve checkmate, the player with the Rook must use their pieces strategically to control the board. The Rook can cut off the opposing King’s escape routes, while the King supports the Rook. This combination allows the player to gradually force the opposing King into a corner, ultimately leading to checkmate.