Yeah I'm not getting it either... if it's really black to move all he has to do is push his pawn to g2 with check. White king must go to g1. Then he takes the f-pawn and marches down the board. White can queen first if he wants to but it's going to be a pawn-duo + king checkmate.
Now how do I insert a pgn which starts at your position?
EDIT: Thank you Sensei Meadows
Black suffered from what so many on here suffer from.
Move Priority.
The strongest thing you can have in chess is the move.
They look at their opponents threat first and deal with
it often missing their own much stronger threat.
He just looked at White's threat of Queening and stopped there.
Check all checks!