It looks pretty impressive, but this trick is nothing more than "hot ice." It's been making the rounds in kitchen science for a while. It's perfectly safe, but takes some preparation and a willingness to air out your kitchen. The substance is sodium acetate, and it's what's leftover when you combine baking soda and vinegar.
The difference between this experiment and your basic homemade baking soda and vinegar "volcano" is heat and patience. As soon as you mix baking soda and vinegar, it combines and forms sodium acetate, some water, and some carbon dioxide. It's the rapid production of carbon dioxide that fluffs up the concoction, making it bubble over the walls of its container. In this experiment, you're going to put some vinegar on the stove, heat it up, and mix in the baking soda little by little. You'll only need about four tablespoons of baking soda for each liter of vinegar. Once the baking soda is in the vinegar, boil (or just heat) the substance until you see a crystal "skin" form on top of the surface. This can take around an hour, so open the windows and sit back. Skim the skin off, and save it for later, then pour the liquid into a container to let it cool. Be sure that there are no extra crystals floating around in the liquid. If there are, add just a bit of vinegar or water to help them dissolve.
Once the liquid is cool, take those saved crystals, put them in a dish, and imitate Uncle Stephen. The resulting "hot ice," which forms as the supersaturated solution crystallizes, can be melted down again and reused. I would not suggest using it in the way Fry suggests. If you do, and if it goes wrong - go sit in a hot tub or something.