According to one of the comments, the animation was created by the user who posted it (user '3D4U'), "using two commercial applications: Cinema4D and After Effects." The about page for this user merely states "Channel hosting a collection of CGI." If you wish to know more about why they made this particular animation, why not just ask them directly?
The green lines you ask about (they are vaguely heart-shaped curves encircling earth, one of which makes a sharp corner at L2) are called equipotential surfaces. Think of them like terrain contours. Each curve has an associated energy level, and any item that is placed on one of the curves (and that is co-rotating with the system, I think...) will have the same amount of gravitational and potential energy regardless of where on the curve it is placed. It will also feel a net gravitational (or centripetal) force towards (or away from) the system that is perpendicular to the curve. Where these curves intersect, the forces balance out and create a Lagrange point.
There is a link in the video description box that takes you to a page that provides more information on equipotenital surfaces, and draws many more than just two of them. Looking at the more detailed set of curves here should be much more intuitive: