EDMX is Visual Studio’s “container” for all things about your Entity Data Model.
It contains all the information that is in the CSDL, SSDL, MSL, plus information about the visual layout of the tables in your Visual Studio designer surface.
The EDMX file is converted into CSDL, SSDL, MSL (typically embedded as resources in your assembly) during the build process. You definitely don’t have to distribute or copy the EDMX files anywhere for the app to run.
Update: if you are more interested in a code-based approach, you should check out the code-first CTP for Entity Framework which gets by without any .edmx, .csdl/ssdl/msl files at all.