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.