It's apparently supposed to work as a capacitor, but I don't see how it would...
I'm calling shenanigans. I would test this, but in my house a potato is harder to come by than a lighter from 7-11 :jerkit:
Yeah, I don't buy the capacitor explanation either. Capacitors still need a charge to store, and I don't see how it could function as a capacitor anyway.
It kind of looks like it's a battery, but generally when people make those they use two leads of different metal. Those ones looked the same. I think it could work as a battery and output more voltage than a potato normally would by being a better electrolytic compound, but if that was the case, what's the point of the potato?
The explanation I've heard that sounds most plausible...
The salt is giving off ions as it becomes "aqeuous" in the toothpaste. Or otherwise as it dissolves. This would explain why it would build up a charge over 5 minutes.
To me that makes the most sense. I've seen potatoe batteries and they barely ever get a single volt, so to me it makes sense that the salt and toothpaste are reacting and causing extra energy.
Then at the end, when the two leads form a circuit, heat just builds up dramatically. You can try this with a D battery... Just put one lead on the positive, the other on the negative, and rub the ends together for a few moments. They should get red hot; put some cotton on there and I have no doubt it would ignite. It's really the same trick as using a flash-light bulb to start fire except you're building residual heat in the closed circuit. With steel wool, it completes that circuit, overloads and ignites; with cotton, you're counting on the leads to get hot enough to ignite the cotton.
So all in all... If you wanted to adopt this as a survival method, a D battery and two small leads coming off the terminals would be all you need--and even then I think that may be a little more redundant than other solutions, but I guess it's one for the "always bring 5 ways" ideology. You could count on a flashlight too, but why not use the flashlight for what it was intended for?