Diet Coke, like most soft drinks, has a lot of carbon dioxide (CO₂) dissolved in it, which is what gives it fizz. When you open the pop bottle, it normally takes an hour or so for all the CO₂ to evaporate as gas bubbles.

If you add something with a lot of sharp surfaces, it helps get the gas out more quickly. It turns out that the chalky Mentos has a LOT of sharp points (under a microscope) so all the dissolved CO₂ turns to gas at the same time. The pressure isn't high enough to blow up the bottle, but you can make a nice fountain out of it. If you have a computer which can show video, these two guys made a complete musical fountain show, like the famous Bellagio fountains in Las Vegas:

The Mythbusters (a very cool science show in the Discovery channel) did an episode revolving around this very question.If you can, I would suggest watching that episode if you want to learn more about the reaction, it was episode 57. The surface of mentos are very jagged, not smooth at all. All those jagged pits and holes make what are called "nucleation sites," which is a fancy term for places where the dissolved CO2 gas in the soda can come out of the soda and make bubbles. Since this can happen in so many places at once, you get a whole lot of bubbles trying to come up through that little opening in the top of a soda bottle all at the same time, and that's why you get the geyser.

"Other active ingredients in the reaction include aspartame (artificial sweetener), potassium benzoate (preservative), and caffeine in the Diet Coke; and gum arabic and gelatin in the Mentos.

The ingredients seem to have a perfect compatibility with each other. When mixed together and added to the nucleation, they create a chemical reaction that forces the soda to release all of its dissolved carbon dioxide at once, thus causing a more violent eruption than carbonated water alone."