The sight of the two bishops both aimed at the king’s position should be food for thought even if one of them is blocked. Here you see that the c4 bishop is obstructed by its own knight, which suggests the familiar possibility of a discovered attack—perhaps a discovered check or even a double check. What tools does White have at hand to push the position along? The crucial piece is the rook on g1, which is poised to be forfeited to the cause. Thus 1. Rxg6+: a classic rook sacrifice on the g-file intended to pry open one of the adjacent files when Black recaptures. If Black plays h7xR, White mates in classic fashion with Qh8. If Black instead recaptures with f7xR, he has opened the diagonal leading to g8, so now that double check with the knight works: indeed, Ne7 is mate.

So long as the king is stuck on those two squares on the back rank, bishops running at those squares can finish it. The special power of the double check at the end of this sequence is that it prevents Black from thwarting the mate with a capture or interposition. The double check requires the king to move, and it can’t.