Those are for the CommNet communications network. They show the connections between your craft and Kerbin.
See that icon in the top left corner closest to the right that looks like a craft, 2 satellites, and a planet with those green lines? That allows you to cycle between no CommNet visualization, first hop, and the entire network (and maybe one more option. It has been a little while since I have played KSP)
Ben J. Kerman's post in All command pods missing after attempting to install Konstruction-Please help!!!!! was marked as the answer