Since Windows Phone 8, developers can register a handler for file extensions.
This is my old answer. It is only valid for Windows Phone 7:
Windows Phone uses something called "isolated storage". This is a virtual storage space created on the internal storage by each application that needs to save files onto the phone. Every application can only read and write to its own isolated storage space. So no other application can see or use other applications files.
There are a couple of special cases. Some applications have associations with other applications. Such as the browser and the email reader that can make other applications save a file of an certain type into its own isolated storage and show it for the user. For example if you download a PDF file in Internet Explorer the PDF reader will download it to its own isolated storage and then the PDF reader will launch and show the file for the user.
As far as I know, external developers can not associate their own programs with other programs in this way. So if I were to make an NES emulator I can't make the phone automatically start NES games, which were downloaded in Internet Explorer, within my NES emulator application.
So all applications that have the need to use files from other sources have to have their own way of retrieving them from this source.