Figure[White to move]

White’s knight on e4 masks the paths of his rook and queen (it's an example of something nice that can happen with a knight in the center); the queen is the more important piece, of course, because it has the king as a target once the knight moves. How to exploit this? If the knight goes to f6, then of course Black takes it out and avoids the check with KxN. But don't give up. The king’s position doesn't look as constrained here as it did in the previous position, but its mobility still is quite limited because White has several pieces bearing down on it. If there is a mating net to be created, every move in it almost certainly will be a check; so imagine going through with 1. Nf6+, KxN, and then examine any checks White would have and their consequences.

The most useful of those follow-up checks would be 2. Nh5+. As you consider Black’s reply you might imagine a dark line leading through the squares on the White queen’s diagonal and another line all the way down the e-file, since those squares all are off limits to the king. And g7 is off limits, too, because it’s attacked by the knight. In fact the king’s only flight square would be f7. Now look for White’s next check, keeping in mind that every square adjacent to Black's king is under attack except g8. Qh7# seals off that square and attacks the king as well, leaving it nowhere to go and ending the game.

The position is a good illustration of how a king can be tightly constrained even when it has lots of empty squares nearby—if those squares are under attack. It takes some practice to get the hang of seeing this; it's worth a little time.