How can a bishop and king work together to achieve checkmate in a game of chess?

In a game of Chess, a bishop and king can work together to achieve checkmate by coordinating their movements to corner the opponent's king and limit its options for escape. The bishop can control diagonal lines on the board, while the king can provide support and help to trap the opponent's king. By working together strategically, the bishop and king can create a situation where the opponent's king is unable to move without being captured, resulting in checkmate.