"
I make my run
At the break of day
He runs out the door before he can be caught. Within the context of this song, Santa appears to be after "little girls". By identifying himself as a "back door Santa", he is making a sexual reference, and while normally "little girl" is bluesy slang for a girl who's physically developed but innocent, this has a more sinister ring to it because Santa is normally associated with children.
It's unclear whether this is actually describing a pedophile, or whether "little girl" is actually more along the lines of the typical colloquial reference.