I study nucleation, but mainly via modelling on a computer. The guy below, Harley Morenstein, took a more personal approach. Incidentally, if you are bored of the Vine looping just click on it.
Drinks like Diet Coke, lemonade etc, are carbonated, i.e., have carbon dioxide pumped into them under pressure to make them fizzy. If you carefully take the top off and are gentle with then (as opposed to giving them a shake) most of the carbon dioxide remains in the drink. This means that the amount of carbon dioxide dissolved in the water is actually above the solubility of carbon dioxide in water (at atmospheric pressure), and so this carbon dioxide wants out (technically speaking it is thermodynamically ‘downhill’ for the carbon dioxide to leave the water and go into the atmosphere).
The carbon dioxide comes out as bubbles and if the drink is not shaken these bubbles can find it hard to start to form. This initial step when a tiny bubble starts to form is called nucleation. If nucleation is not possible then this traps the carbon dioxide in the Diet Coke or whatever the drink is.
Until something comes along to make nucleation easier, like Mentos. Mentos are an American sweet, and for reasons nobody really understands, carbon dioxide bubbles nucleate like crazy on the surface of Mentos. So when the guy in the Mentos suit drops into the Diet Coke tub, bubbles of carbon dioxide nucleate like crazy, and you saw the result above.