You may have heard of mashups before.  An anime music video is a special version, wherein Anime (or other kind of animation) is edited to be co-ordinated with a specific song (or other, completely unrelated audio source).  I discovered them while looking for something else, and have to admit that I was surprised by the artistry and results of many of them.  Judge the results below.

I guess we will have to start rethinking copyright, for example.