What does "A bigger boy ran in the back door, and kicked it to." mean?

"kicked it to"  ==>  kicked it to normal condition {closed}  [or to the closed position]

It means he kicked it shut

Essentially nothing.  "He kicked it to" what?  He already ran IN [through] the door, so why did he kick it?

It may mean that Google Translate failed you again

He kicked it to close it. 

It doesn't say if the door was kicked open or kicked shut.  It was kicked to. "kick to" means to force into place by kicking.  Is the place in this context the door fully open and up against the wall, say, or fully closed and latched so not easily opened?

The meaning is that the bigger boy, one of the other boys who was bigger (than Billy), was the one who kicked the door into place, whatever place that the kicking was  intended to put it to.  If they were trying to get in, the kicking to would imply kicking the door wide open, but if they were trying to shelter inside, kicking it to would mean to slam it firmly closed.

It reads like a smaller boy tried to kick the door open first and a bigger (stronger) boy was needed to kick the door open.