The explosion created when soda and Mentos are combined occurs because of nucleation, a process in which the carbon dioxide in the soda attempts to latch onto the outside of the Mentos, creating a huge amount of pressure. This pressure forces the soda to explode out the top of the bottle.
The carbonation in a bottle of soda exists because of a large amount of carbon dioxide forced into the small space of the bottle. The carbon dioxide in the soda is attracted to bumps or nooks to connect to; these connection spots are called "nucleation sites." When Mentos are dropped into the bottle of soda, they offer a huge number of nucleation sites in a very small space. The exteriors of Mentos are coated in a rough layer of sugar, which provides numerous sites to which the carbon dioxide can link.
As the volume of pressurized carbon dioxide rapidly rushes toward the Mentos, it creates a dense concentration of carbon dioxide bubbles around the Mentos. As the Mentos continue to sink, this reaction continues throughout the bottle. This pressure rapidly reaches a point that overwhelms the capacity of the bottle, forcing a stream of soda through the opening.
The physical reaction between soda and Mentos depends on the specific ingredients used. Diet sodas tend to produce a stronger reaction, which is typically attributed to the higher carbonation levels in these options.