In Diagram 6.1, White may move the bishop to any of the dotted squares or may capture the rook.
Not all the squares are safe. If White played 1 Bb6+, Black would capture with 1 ...Kxb6. Of course the most obvious move for White is 1 Bxg7, winning the rook.
Each player starts the game with two bishops, one on a light square and one on a dark square. As you can see from the diagram, a bishop on a dark square can only move to other dark squares. Similarly, a bishop that starts on a light square will only ever be able to move to other light squares.
A king in the corner has only three escape squares and in Diagram 6.2 they have all been taken away.
The white king cannot move to g2 or h2 because those squares are attacked by the black king. He can't move to g1 because he would be in check with the e3-bishop.
Black can deliver checkmate by playing 1...Be4#. The king is checked by the bishop and cannot move out of check.
If it was White's turn to move in Diagram 6.2, the result would be a draw by stalemate.
In Diagram 6.3, White mates with 1 Bc5# (1 Bh6+ is not mate because Black can play 1...Rg7).
In Diagram 6.4, Black mates with either 1...Bh4# or 1...Qd2#.
Any rook move in Diagram 6.5 will leave the king in check with the bishop. White mates with 1 Rb4#, using the rook to attack the black king's escape squares on the b-file.
