The chorus.
Sorry, just couldn't resist. As for the connection between the line and the rest lyrics I assume it's either a reference to the period. The song is set in autumn, when the man comes back to approach his love-interest, but she runs away from him, the demon. Hence, demon of the fall. Or it has to do with his own from "grace" so to speak, this is where she totally shuns him, and he's thus fallen.
Maybe.
I've come to realise that some Opeth songs are not meant to be dissected, appreciate it for the mood alone.