(At the risk of sounding glib, the photo makes this much clearer than words can explain it.)
The twist: Rather than rotate horizontally through a monster hinge on the base, Dell's hybrid screen is designed to flip 180 degrees vertically through a central axis within the frame of the lid, letting the LCD face either forward toward the keyboard or away from it. Dell pioneered the unique swiveling screen in 2010 as the Inspiron Duo, a hybrid Windows 7 laptop and tablet.
If the Dell XPS 12's design looks familiar, that's because you've probably seen it before.