Blacks first priority is to prevent the white king from getting to g6, because black cannot dislodge it from that square and although the extra pawn on the queen side means that black is still winning, it will be a slow grind.

So the first move from back needs to be a king move. King h7 prevents Kg6 but it is no longer forced mate because white can sacrifice the bishop with bxf6. If black recaptures with gxf6, then black is again out if ways to checkmate because he cannot get to the white king on a light square. If black ignores the bishop and just goes g6+ immediately, the white king can escape via Kxg5 and again no checkmate in sight.

So that only leaves us with Kf7. Now if white plays anything else that Bxf6, g6# is checkmate, so Bxf6 is forced. If black now recaptures with the pawn gxf6, again he is out of pieces to attack the king, so Kxf6 is the only move that will continue with forced checkmate.