The mentos is covered with small holes, similar to a catalyst. These allow the carbon dioxide in the coke, which make it fizzy, to come out of solution very quickly, and as this increases the pressure inside the bottle, there is a rush to exit the bottle through the small bottleneck, resulting in a fountain of coke.
Diet coke is better because the sugar in normal coke helps hold on to the carbon dioxide, as it is a very large molecule that traps the carbon dioxide, so it is released at a slower rate.
Also, fruit mentos won't work as they are glazed and so do not have the small holes to bring the carbon dioxide out of solution.