The cluster of White’s bishop and knight on e4 and f3 should jump out at you as the possible basis of a discovery (generally speaking, any friendly piece lined up with a knight should get you thinking this way). The bishop has no target yet in place, but since it’s aimed toward the enemy king’s corner, thoughts of a discovered check come to mind. The king would need to be drawn over a square onto the long diagonal. A simple if costly way to do this is by planting the queen on the square where you want the king to go, forcing it to capture there; thus Qb7+ causes KxQ. Experiment with what might come next: Nc5, a double check, forcing the king to move and so keeping all of your pieces safe. What would Black do? The a8 and b7 squares are off limits to his king (imagine a line through that diagonal), and so is a6 (thanks to your knight). So Black would have to play the king to c7 or b8. Now consider White’s next checks in either case. The pattern of those two same-colored flight squares should suggest an attack by the knight, since it can hit them both at once—i.e., with Na6#, finishing the game since White’s rook cuts off the whole d-file.
This is another sequence where White's threat not only is decisive offensively but also does important defensive work by holding the initiative. If it were Black’s turn to play he, too, would have a forced mate: 1. …Qh2+; 2. Kf1, Qh1+; 3. BxQ, RxB#. One way to defend against a threat like that is to launch an offensive sequence of your own, giving your opponent no chance to get in his attack.