Essentially, it will take any solids that are not booleaned together and save them as separate files.
So if you model a nut and a bolt, for instance, exporting without 'multi-file' checked will save them as one big mesh for modo. Checking 'multi-file' will save each solid - the nut and the bolt - as two separate STL, DXF, etc. files in the chosen directory.
These separate files should maintain their spatial relationship so that when you import them into another program, they fall right into place!
I use this a lot for exporting to Maxwell - I ensure the major parts with material differences are saved separately.