When you purchased your phone and got home you set up a google account. That account is remotely linked to your phone. If you purchase an app from the play store it will be visible from wherever you sign in to your account. You can't pass that app over to your girlfriend. She has a google account and you have a google account. If your phone was stolen or lost you could easily add every application you ever downloaded by signing in to your google account. No cables needed, but you can't give each other apps.
Sent from my SAMSUNG-SGH-I727