The first thing I ask of anyone interviewing with YC: Do you have a demo?
If you don't have a demo, you're going to have to describe your vision in a very short span of time and under pressure. Your demo, presumably, won't be shaky or easily confused by pg's questions (which I was pretty much always thrown off by, as they weren't the things we came in expecting to answer or talk about), and will just work. Even a mockup is better than having nothing, though not by much.
Having a demo exhibits so many things that are impossible for them to really judge in any other way. It shows you're committed to the project enough to spend some of your own time on it. It shows you're capable enough to build the things you say you're going to build (or at least a reasonable start on those things). It shows that you've thought enough about the idea to produce a prototype, which gives a much better view of the workability of the concept. And, finally, it helps them to understand what the heck you're talking about--they're hearing dozens of pitches on the interview weekend, and will be far more likely to remember what you're doing, if you show them than if you merely tell them.
Great point, I definitely endorse that point as well. We didn't have a prototype when we applied, but we created one by the time we were interviewed. Showing even a rough prototype will explain your idea better than anything you say during that 5 minutes.
I do wonder about the demo. All is well and good if it works with no glitches, but what if a spectacular bug catches you out when you don't expect it and the whole thing blows up in your face?
By limiting the scope (rather than the maturity) and testing heavily you can be reasonably confident, but it will leave you with a less impressive demo to throw up.
I think you should view the demo as a much more efficient way to express your vision, rather than thinking of it as a way to impress. The latter doesn't hurt but it isn't as useful towards conveying what YC would like to hear.