This position doesn't contain the clues we usually associate with a back rank mate. You only would be likely to see the idea for Black by examining any checks he can give. His checks with his queen all lose the piece, but then there is f4-f3+: the pawn can't be taken, so it forces White to move his king. If he moves it forward, his rook is left unguarded and Black has QxR; indeed, one way to see the idea here is to start by observing the possible capture QxR, to notice that the king prevents it from working, and so to think right away about checks to drive the king away. In fact Kg3 turns out to be White's best option, for if he instead moves the king back to g1 he ends up mated. Do you see why? Once Black’s pawn is on f3 it seals off both g2 and e2; the king is trapped on the back rank. So Black plays QxR+, suffers the recapture KxQ, and now mates with Rd1. The general lesson is to see how an advanced pawn can cut off a king’s escape just as its own pawns would.