Boring Scientific Explanation

Officially, the reason this effect works is not really a chemical reaction. In order for the dissolved carbon dioxide to escape the liquid, it needs a "nucleation site ", which is someplace rough where the carbon dioxide can gather. (This is essentially the same reason some people seed clouds to make it rain.)

Mentos have two qualities that make the soda "explode". First, they have a rough surface that give the carbon dioxide a lot of nucleation sites. Second, they are relatively dense, which allows them to quickly fall through the liquid and release more gas.

So, the Mentos fall through the liquid, giving the dissolved carbon dioxide thousands of nucleation sites all at once and thereby realease much of said carbon dioxide all at once. Since it has no place to go, it all goes out the top as quickly as it can, taking a whole bunch of the surrounding liquid with it.