With a one-button app, you achieve your primary goal with just one button push. No click click click check select check click submit. Just "do it." Todd's favorite personal example is the Flashlight app for the iPhone. Press a button and the light comes on. It's one of the few apps he liked enough to buy the premium version.
Twitter is a one-button app. Type and send.
Angry Birds is a one-button app. Stretch and let fly.
There's a reason Amazon patented and fights to protect 1-click buying.
If your product isn't a one-button app, how can you expect anyone to really get it in a 5 minute pitch? If your first testable release isn't a one-button app, how can you tell what your users really feel about your core value proposition, and not other issues?
Take the example of reserving courts (basketball, tennis, squash, etc) on a college campus. The general solution is a classic calendar-based event scheduler, where first you have to select the type of court, to get the calendar of reserved times, then do the usual time selection rigamarole -- and you haven't even contacted the people you want to play with yet.
To get a one-button app, first pick a common use case, like arranging pickup games. Those are always the same people on the same court type. When you start the app, all you see are buttons for today's free times for that type of court. Press one of those buttons reserves the court and notifies the people you play with. They get a "can you play at ..." message with buttons to say "OK" or "Can't make it." If too few OK's are registered within the next hour, you get a message and buttons to "Cancel" or "Keep."
That's it. Just one button push to do what you normally want to do. Only on the first use, do you have to pick a court type, and, when you pick a free time, say who to notify. These choices are remembered for future use. They're easily changed, along with many other options, via a preferences panel.
But the core value of the app is in that one button push.