What is NUI?

When it comes to Microsoft Surface, there is always talk about natural user interface (NUI). I'd imagine that there are a fair number of people out there who don't understand what NUI is, or maybe have some mis-conceptions about what it is. In the video below, I get our friend's at Stimulant's take on the topic. This isn't a plug for their work, but an open discussion of what NUI means in general and for Surface. Do you agree with the interpretation? What are your thoughts on NUI aside from the buzzword?