In layman’s terms here is what is happening:

It is a reaction of the Phosphoric Acid contained in the coca cola to the milk. Phosphoric Acid molecules attach to the milk giving them more density and separate out while the remaining liquid that makes up the milk and cocoa cola now being lighter floats on top. The solid matter is basically milk that has been curdled by the addition of the more acidic soda.

On a side note the uploader of the video also commented on their own personal observation of soda and its properties in degreasing things and taking the finish off of furniture.

We hope you like the video.