The first thing to see is the b2 bishop’s clear line of attack against h8. Then see the other bishop on b1 also aimed at the king’s position. All the obstructions on the b1-h7 diagonal look discouraging, but don’t be deterred by them lightly; they might be removable, and with a knight on g5 the possibility is important to explore: If the bishop on b1 were on h7, the game would be over. So White goes to work with sacrifices to clear paths: first, 1. Qxh5, gxh5 (to prevent Qxh7#). The g6 pawn is out of the way; that leaves the knight on f5. Again White clears it by making a threat—a check—from a square the knight protects: 2. Ng4-h6+, Nf5xN (again forced). Now only the pawn on h7 is left, so White takes it out with his mating move: 3. Bxh7#. It's just another study in the methodical removal of obstacles to a mating pattern

Granted, all this merely is the sequence that results from natural recaptures by Black; after White’s original Qxh5 Black also can play BxN, allowing QxB and thus sacrificing a piece to disrupt the mating threat.