tekawitha . .  basically a remix takes an existing song and recreates it by adding ones own ideas or blending parts of another song with it as was done with Apologies and Fences.  

The first time I ran across a remix there was a comment with it that explained how popular it has become and had a wikiHow link . . found the link again . .  http://www.wikihow.com/Remix 

There is also a regular wiki entry if want more information . . the history is kind of interesting.