I realized that some of you are having problems visualizing the concept so I made this mock-up explaining all of the possible uses for the NX concept based on the original drawing from Eurogamer.
In this first picture, you can see the NX in its most basic form a simple device that can play simple games like Professor Layton or even Mario Kart with its motion sensors and touch screen.
If you turn it in portrait mode the NX plays mobile games (ported or created for mobile like Nintendo upcoming mobile games.) like a champ.
Once things get more complex let's say, Zelda, you slide in the control modules.
(I think that sliding it instead of attaching it will help with durability) as you can see in this picture each of the controller pieces being connected have their own simple gyros as well and could be used as a Wii-Mote.
In this form, you can play games as you would with a 3DS (but with a full set of buttons) when not using the main unit you slide the controllers in a simple shell in order to have a standard controller.
Now you can use the main unit in its base connected to a TV or use the main unit as a monitor.
And using the stand you can enjoy video apps.
Finally, when connected to its doc outputting to the TV the screen could show some basic info (like the gamepad) or be turned off (like the gamepad) in order to charge faster .
I hope this helps to illustrate the NX concept.