Okay, so the particular idea of Anderssen’s mate is to achieve the result just described by (a) first sacrificing the other bishop—the king’s bishop—to open the h-file, (b) moving your queen onto the h-file, where it gives check, (c) and then dropping your queen down to h8, where it mates. Here is an example: White sees that his queen is one move from the h-file and that he can obliterate the pawn on h7 with his bishop; so he plays 1. Bxh7+, KxB; 2. Qh5+, Kg8; 3. Qh8#. Black’s moves were entirely forced. Notice that with Qh5 White seals off g6 as a flight square.
Examine this diagram until you are clear on the role each White piece is playing: the f6 bishop holds the long diagonal and supports the mate on h8; the queen is ready to land on h8 in two steps; the bishop on e4 goes on a kamikaze mission to take out the pawn blocking the h-file. The two bishops both trained on the enemy king’s position are a clue that this pattern may be available.