
We have a passed g-Pawn here. Thus Black's using standard procedure and blockade it with a Black Queen. Remember, blockade and destroy; but it's too late for Black to destroy the White's g-Pawn. In this complicated position, the center is open, leaving both Black's and White's pieces free access to the corners of each side. The Black bishop at b7 guards the h1 square; whereas the White bishop at c3 is pinning the Black Queen against the Black King at the corner. In addition, the White Bishop at b3 is attacking the f7-Square, the "throat" of the opponent. It also controls the g8-Square such that the Black King cannot slide itself back to its original castled position! Now we have a passed g-Pawn who controls the Black King's flight square at h7 as well as attacking the f7-square with the King's Bishop at b3. Yes, there is a black King Bishop Pawn at f5. This Black Pawn is threatening giving check to the White King. Can Black accomplish this threat? No, he cannot because White shall mate in the next move. All right, but what if Black carried out this threat by f5-f4+, could White have been able to accomplish one of three responses; that is, capturing, interposing, or fleeing? Yes, White could have captured the Black pawn by Kxf4 with the result of King's occupying the f4-square. This is a dangerous exposure for the White King. Fortunately, the Black Rook is at a7 and a1 respectively and they could have been traded off with the White Queen without further endangering the White King at f4! Now, let see the Black Pawn at c7, it is an isolated pawn and it seems to be too late to push it right now. The reason is the White Bishop is also guarding the f4-square. It's much better for the pawn to stay where it is and be protected by the Black Queen :-) You might have wondered how did the Black Rook happen to be at a1. The answer is it's just captured the White Rook at a1.
Now we analysed the whole picture of what's going on. Let's do some specific calculations. What should White move now? Can White do a standard "capture and check" move? Let's see... Yes, White can play Bxg7+ with Black King's capturing back. This looks Ok. Remember, we want to push ourselves. Is there a dearer attacking idea here? More important... Yes, normally, we wanna maintain a pin and attack the pinned piece directly in front or from the side; this is much faster because the capturing piece ususally covers less number of squares to accomplish the "capturing" move. So let's rule out this line of calculation, Bxg7+. Of course, Rh1+ may come to mind; but the whole picture is the center is opened and the corner is controlled by Black's "missile" at b7! So we rule out Rh1+. Going sideways is out of the question now, what about going vertically? Yes, the White Queen can go straight to the opponent's back rank without any trouble! The reason is the back rank is unguarded by a rook or a queen, so it's weak. The White Queen really makes her day by operating on the King file or the e-file. As you know, there are plenty of historical incidents in this file folders where even a lady-Queen could act out as a super-heroine :-) Yes, the right move is Qe8# because the Black King is cornered at h8 from the analysis of the whole picture and the accomplishment of the final calculation.