Well, I will venture a short and more literal answer to your question first, but if you have more questions, please ask !
The "E minor" refers to the scale that the majority of notes used in the piece have been pulled from. You can tell it's in E minor (vs. G Major) because of the last chord of the piece, an e minor chord. In most pieces you can tell what key the piece is in and what scale the key signature refers to, based on the last chord of the piece (there are exceptions, of course !).
Hope that hepls !