The usual scanning turns up a pin of Black’s h7 pawn by your rook. A pinned pawn is an invitation to take something it protects. This one protects the bishop on g6, which now is loose. White’s rook is aimed at it; the impediment to the capture is White’s knight on g5. White’s task is clear: vacate his knight from g5 in a manner violent enough to force Black to spend a move replying to it and not moving or defending his bishop. A check usually is best for the purpose; hence Nf7+—which also forks Black’s queen, and so requires Black to capture the knight rather than just move the king. Black has three ways to take it: with either of his rooks or with his bishop. If the bishop thus moves to f7 by making the capture, what becomes possible? Qxg7#: for notice that White’s queen and g1 rook both are trained on g7; if Black’s bishop moves out of the way, White mates there. The bishop is pinned to a mating square. (Notice that the movement of Black’s bishop not only would clear the way from White’s rook to g7, but also would block the path of Black’s rook to the defense of that square.) Black has to capture instead with one of his rooks—e.g., Rc7xN. White then has e6xR, and RxB a move later.
In this case the pin of the bishop to a mating square only became significant in the course of working out a capture made possible by another pin. The coordination of White’s rook and queen against g7 nevertheless serves a key role; without it the capture cannot occur, since Black replies to Nf7+ with BxN. As usual, the key to seeing this is to notice that White has a queen and rook both aimed at a square adjacent to the king, and not to overlook this because one of the needed lines—the g file—is blocked both by an enemy piece and one of your own. That mating threat in the background greatly restricts the motion of the pieces lying in the way.
You could have tackled this position as well by seeing White’s potential knight fork Nf7+, and observing that this causes Black either (a) to lose the exchange by playing RxN (and suffering the reply e6xR, with more trouble to come) or (b) to play BxN. But you look for your next check if he does play BxN, and find that QxN is mate.