Do you know what Twitter is? It is a service that allows users to make posts of about 50 words and then share them on the Internet.
There is something else called Vine, that is the same as twitter, but for videos. So, users can post very short videos. They are just like tweets, but videos instead of text.
A vine compilation is a video that someone makes by joining together a bunch of these short videos. The phrase "vein compilation" is probably only recognized by a small number of Internet users. I don' think most people would know what it means.