White has a mating threat (Qxh7 Kxh7 Rh6#) that he couldn't execute because he was under check. On the next move Black will remove the mating threat with 1...Qxg6 or with a knight move, most probably 1...Ne8.
With his knight on d4 (after 1.f3 or 1.Kg1), White cannot counter either defense satisfactorily, e.g. 1.f3?? Qxg6 and he can resign. However, the beautiful unguarded guard 1.Nf3!! gives him two more resources: the knight can jump to e5 aiming at a smothered mate from f7, and the bishop gains access to the long diagonal from d4.
1.Nf3! Qxf3 2.Kh2 Ne8 (2...Qxg6 is not possible anymore; if 2...Qe4 3.Qxh7 Kxh7 4.Rh6#) 3.Bd4 Rg7 (3...Ng7 4.Qxh7 Kxh7 5.Rh6#) 4.Rxg7+-
1.Nf3! Qxg6 2.Ne5!! Qe8 (2...Qxh6 3.Nf7#) 3.g6 Qxg6 (otherwise 4.Qxh7#) 4.Nxg6#
1.Nf3! Qxg6 2.Ne5!! Qe4 3.f3 Qxe5 (otherwise 4.Nf7#) 4.g6 Qa1 5.Kg2 followed by Qh7#
1.Nf3! Ne8 2.Bd4+-
White wins in all cases. Very nice combination.