Figure[White to move]

White has a traditional threat: a queen and a minor piece aimed at a square next to Black's king (c7). Qxc7# is prevented by Black’s queen on c5. Two trains of thought leave from here. The first is simply to imagine going ahead with 1. Qxc7+, QxQ, and asking what checks you would have after that forced exchange. There would be one with your d2 rook (Rd8) and another with your e2 rook (RxR), neither of which helps; but then there also are two with your knight—Nd6 (no good) and Nxa7, which is mate because the d2 rook seals off the Black king’s flight squares.

The other way to see this is to focus on the Black queen that prevents mate in the first instance and ask what other duties it therefore cannot perform—whether it protects any other pieces, pawns or important squares that you can exploit. You see here that Black’s queen also protects the pawn on a7; more to the point, you realize, it protects the a7 square on which White’s knight otherwise would mate. Once you realize Black’s queen is guarding two different mating squares the position just becomes a matter of figuring out which threat to use first.