First you need to see White’s mating threat, so start by studying Black’s king. When a king has a protected enemy pawn in front of it like this, of course, its flight squares to either side are sealed off. Since the other nearby squares are occupied, the king’s only range of motion lies along the light-squared diagonal leading to e8; this means that an attack against the king along that diagonal has lethal potential. White can launch such an attack with Qxh5; indeed, that move would be mate were it not for the protection provided to h5 by Black’s queen. Can you block the Black queen’s path to the mating square? Yes, with Rf5 or Nf5. Either works, but let’s focus on Rf5; consider Black’s reply options and their consequences:

(a) If Black plays e6xR, White’s mission is accomplished: h5 has been left loose, and now he mates there with his queen.

(b) If Black plays QxR, White has NxQ (and an eventual forced mate).

(c) Or Black can forget about his queen and take out the mate threat directly with Nxf6, attacking the h5 square where White wants to put his queen. So White doesn't bother with that; instead he is content to play RxQ.

As often is the case, seeing a sequence that can lead to mate thus pays off not with mate but with sacrifices by your opponent to prevent it—an entirely satisfactory result.