By now the vulnerability of Black’s king in this position should be obvious: it has no flight squares; an attack against it on either of the light squared diagonals leading to its position has mating potential. If White puts his light-squared bishop on b5, Black stops him by interposing a pawn on c6. So White turns his attention to the other diagonal and the possibility of Bf7, where the bishop mates but for the Black rook guarding the square from h7. Fine: now White has a target in Black’s rook. He has a way to attack it and take something it protects with Qxh5, but to this Black can reply g6xQ. So White works backwards and sees that he first needs to get rid of the g6 pawn by taking something it protects. He therefore begins with 1. RxB. Black’s only recapture is 1. …g6xR; and now White plays the fork 2. Qxh5+ (notice that the movement of Black’s g-pawn extended the open line to his king) and mates with Bf7 next move no matter what Black does. (E.g., Black plays RxQ, and then White has 3. Bf7#.)
Now of course if Black sees this coming he will not reply to White’s initial RxB with g6xR. He will play something like Qd6 or Nd7, refusing to move his pawn on g6. So White wins a piece. Again, however, the fruitful train of thought started with the mating idea and worked backward from it—not because the sequence ended up achieving mate, but because it would have achieved mate if Black recaptured every time you captured. It is the threat of mate that forces Black to forfeit material in order to stop you.
This is another of those positions which could fit comfortably in the next chapter on attacking the guard, but it fits here as well because in the end the Black rook is overworked: it protects the mating square f7, but also what turns out to be an alternative mating square for White's queen: h5.