Actually, the OP was quite specific - the Media Browser is a function within iMovie to be able to share movies to other Media Browser enabled applications, like iDVD, iWeb (basically sharing between iLife applications). Basically, it renders the movie and makes it available to those other applications. In terms of where it stores it physically on the hard drive - it appears to be just referenced by the media browser, and is actually stored within the package that the original save was done.
So, let's say you had a project: Great Movie
under "~/movies/iMovie Projects" there would be a package called "Great Movie"
Within the "Great Movie" package, there is a subfolder called Movies. In there is the Media Browser export.
Using Media Browser is only effective really if you want to share for iLife apps like iDVD, iWeb and anything else that is media browser aware and can use video. If you want to export it for other things - whether to just have sitting on your desktop or to youtube or whatever - one of the other export options is more suited to the task.