The new documentation that will be online soon (it should have been online already but was postponed because of illness in the ez.no crew) will explain this in detail.
The crash course is as follows: Index.php always handles the eZ publish requests. Basically index.php then runs the url through our nice URL engine. Your url "media_files" is then translated into what we call a system url. The system URL will in your case probably look something like "content/view/full/21". (You can use system url's directly from your browser if you like.. but then you need to know the node id at the end).
The system url tells you the module and the view to run. In your case it is the module "content" and the view "full". The rest of the URL is forwarded to the view as parameters.
After translating eZ publish runs the module and the view. In the case of the content module you should look at the files in the directory kernel/content/. module.php defines the various views etc.
The view loads and generates output via a template. The module output is given back to index.php which loads the main template pagelayout.tpl which outputs the module output wherever the user specified.
That should explain how a basic page request is handled with eZ publish. In case of input to eZ publish look at the "actions" that are also defined within module.php.
