Figure 6.1.8.4[Black to move]

Let's stretch out the current logic a bit. You should see Black’s rook ready to move to e1, and consideration of the check Qd4 also should be automatic: it’s safe, and it forces White to move his king to h1; any check with those properties cries out for careful study. (If White instead interposes with Rf2, he walks his rook into a pin; now Black mates with Re1.) With White’s king pushed into the corner, the remaining question is how to take advantage of his weakened back rank. Re1 doesn’t work because White’s rook still is on f1. And Black also has no safe way to move his queen to the first rank. The solution is Qf2, where Black plants his queen on the penultimate rank and puts White to a bad choice: if he plays RxQ, Black mates with Re1 followed by RxR (after White moves his rook back down to f1). Yet otherwise Black threatens QxR#.

Since Black's Qf2 isn't a check, White does have a way to avoid mate by generating counterplay at the other end of the board: Qxf7+. Now if Black plays KxQ, White has RxQ+, with the check gaining him the safety of a tempo. So Black doesn't play KxQ. He plays QxQ, and now White dares not recapture RxQ because then he once again gets mated by Black’s Re1. White instead has to let go of his queen and play Rg1, which saves the game for the very immediate future but at catastrophic cost. Playing this one through in your mind’s eye a few times is a useful exercise.