It's still not completely clear what characterizes the sensation of carbonation. People assume carbonation is the feeling of bubbles popping on the tongue, but when people drink carbonated beverages in a pressure chamber, where bubbles don't burst, they describe it the same way. So it's not purely mechanical.
Chemically, adding CO2 to water creates carbonic acid, which is tasted by sour-sensing taste cells. Research has suggested that a certain enzyme, carbonic anhydrase, sits on those cells and reacts with the acid to cause carbonated water's familiar popping sensation. (Fun fact: climbers who take altitude-sickness drugs that block the enzyme, then drink champagne, report the bubbly as having a dishwater-y taste.) That enzyme, combined with a reaction occurring in the body's trigeminal nerve, could be what gives carbonated water its unique sensation.