This is how my mesh looks when selecting either my character's body, just the head, or just the torso. I know from working with puppets others have made (and some that I've made) that it doesn't normally look like this.
I don't know if this is related to any of the problems I'm learning through.
A "mesh" is a group of layers in the puppet hierarchy that are not independent. As soon as you mark something independent, a new mesh is started. The arms are legs for example are probably marked as independent. The Head however is not marked independent, so it is included in the same mesh as the body. There is nothing wrong with this - it is up to your puppet design whether you want the head to be independent to the body or not. If you want the head to rotate left and right without the body moving, then you want the head independent (+Head). If you don't want this (you want the head stuck to the neck so the body moves with the head movements) then your puppet is set up correctly.