The mating threats get a little more involved as we go along. This time White doesn't have two pieces aimed at a square adjacent to Black’s king. But if you study the king’s position you find it notably constrained. His own pawn blocks f7 as a flight square; White’s pawn on f6 seals off g7. So an attack on the back rank would push the king onto h7, its only available square. Look for checks you could give against the king in that position and see that Bf5 would be mate. So the idea of a back rank combination comes into view.

The difficulty is Black’s rook on a8, which guards the back rank and so prevents White from starting the process just described with, say, Qe8 or Rd8. When an enemy piece stands between you and a mating idea, a first thought is to capture it. This White does with QxRa8+. Black recaptures NxQ, but winning material wasn’t the point; the point was to follow up with Rd8+. Black’s king is forced to h7 (the interposition Re8 is useless, as it just results in RxR+ and the threat is renewed), and now comes Bf5#.

Lesson: when the king’s range of motion is limited, consider whether you can force it onto particular squares and whether you would have additional ways to attack it once it got there. If such things would be possible but for some enemy piece that prevents them, turn your attention to the enemy piece. It may be as good as pinned to its position; or, as here, you may simply be able to capture it.