THINGS TO TRY
What two screens let you do.
The outer display is not a smaller copy of the inner one. These are the things it makes possible, taken from what Apple has shown and written.

CAMERA
iPhone Duo camera tricks the outer display makes possible
The person you are photographing can finally see the shot.

FACETIME
Dual Capture in FaceTime: show a room and your face
Show the room without vanishing from the call.

SAFARI
Open two Safari windows and compare without switching
Two listings, one screen, nothing to flick between.
How to read these.
Each one is a thing you can try on iPhone Duo, described from what Apple has shown or published rather than from our own testing. Where Apple has not said something, the page says so rather than filling the gap.
For the mechanics underneath, the guides go deeper. For which apps can do what, start with the directory.