The basic idea is that on every computer system there is a convention about how files corresponding to Mathematica contexts should be named. Then, when you refer to a file using a context, the particular version of Mathematica you are using converts the context name to the file name appropriate for the computer system you are on.
|name.mx||file in DumpSave format|
|name.mx/$SystemID/name.mx||file in DumpSave format for your computer system|
|name.m||file in Mathematica source format|
|name/init.m||initialization file for a particular directory|
|dir/...||files in other directories specified by $Path|
Mathematica is set up so that will automatically try to load the appropriate version of a file. It will first try to load a name.mx file that is optimized for your particular computer system. If it finds no such file, then it will try to load a name.m file containing ordinary system-independent Mathematica input.
If name is a directory, then Mathematica will try to load the initialization file init.m in that directory. The purpose of the init.m file is to provide a convenient way to set up Mathematica packages that involve many separate files. The idea is to allow you to give just the command , but then to load init.m to initialize the whole package, reading in whatever other files are necessary.