First see the elements of the mating idea: Black’s queen cuts off the empty g2 square, so White’s king is stuck on the back rank; but Black’s rook can’t get there because his own bishop is in the way on d1. Yet the bishop has the power to play the same role that the queen currently does, and that suggests a way to vacate it to make room for the rook: the bishop could be moved to f3. Playing that move straightaway wouldn’t work because it wouldn’t force anything; usually for a sequence like this to be effective every move has to be a check that holds the initiative. But that can be arranged by first drawing White’s king onto h1. Thus Black begins 1. …Qh1+, forcing KxQ; now 2. …Bf3+ gets the bishop into the right position with another check that forces the king back to g1. This leaves d1 vacant for Black’s rook, which arrives there and mates. It’s all very useful for Black, not only because it delivers checkmate but because it saves him from being mated himself via Qxg7.