In my opinion they encourage the story to move on. Minor characters include friends, family, loved ones...things like that. These people all encourage the protagonist(s) to move forward. I mean, if the protagonist didn't have any of these, how are you going to be interested in an antisocial person who doesn't have a family and doesn't love any other living soul? (No offense to those of you who do that, this is just an example!)
I hope I helped! ^_^
