White’s queen is loose and under attack; then again, Black’s queen also is loose. So you might naturally be inclined to play 1. QxQ. What’s wrong with this? Consider your opponent’s threats—especially any checks he can give—and you see his reply 1. …Nf4+, a discovered check that lets Black win back the queen next move: 2. Ke1, NxQ. White still does well: 3. RxR+, RxR; 4. NxR, KxR; 5. Ke2 and 6. Kxe3 and White has won the exchange and a pawn.
But the really important question is whether you can resist being mesmerized by these possibilities and instead step back and observe the constrained position of Black’s king. It cannot move, and there is an open diagonal running toward it; this raises the thought of Qd5+, a move that would mate but for the Black rook on d8 that protects the mating square. But don’t stop there, either; see that White already has two pieces trained on f8, and also would be prepared to mate there with RxR—again, but for Black’s rook on d8. So the d8 rook becomes the focus of White’s energies. He would like to threaten it in a fashion that forces it to leave the defense of one of the two mating squares, f8 or d5. Attacking it with a check would force Black’s reply helpfully, and the way to achieve this is suggested by those dual threats just described. We said that White’s 1. Qd5 was a threat of almost-mate, but at the same time it also is a queen fork of Black’s king and rook. Black is forced to reply RxQ, and now he has left the way clear for White to play 2. RxR#. (Black also has the option of playing the useless interpositions Qe6 and Rf7; White’s queen just eats them up.) Thus 1. Qd5 leads to a quick mate for White.
This is another example of a point we emphasized earlier: the importance of looking beyond the first mating idea you see and inspecting for more. If you saw one of the possibilities here but not the other, you would miss out on a chance to end the game.