Quoted By:
The pokemon world is elementally unstable. If you're connected to the elements, you can change them - manipulate the weather, turn air into water or even summon a tidal wave in a desert.
The games show this with Groudon and Kyogre - they're not actually all that powerful by themselves (heck, most people catch one of them), but their abilities to manipualte the weather without any effort relies on their deep connections to the elements.
The anime shows it clearly with the many mysterious forces throughout the world - the Dragon Force in M14, the Aura of Lucario and the aura guardians, and so on. As early as the second movie, we see Lugia and the three legendary birds as the very embodiment of tides, storms and ocean currents.
My guess would be that pokemon like Blastoise just have organs that tap into the primordial element of water like a red dragon in D&D has an organ that's more or less a portal to the Elemental Plane of Fire. Only in the pokemon world, the elemental forces are not outside the world, but ingrained in it - so provided you know how and have the connection to the elements, you can manipulate the world around you as you see fit.
