Fanta is fizzy because it is carbonated, as it was originally developed as a replacement for Coca-Cola. Fanta was invented in Germany during World War 2.
During the war, Coca-Cola in Germany was unable to import Coca-Cola syrup from the United States. The company's head decided to create a new soft drink that used ingredients available in Germany at the time.
Fanta's fizziness comes from carbonation, which involves dissolving carbon dioxide into a liquid at high pressure. Once the pressure is released, gas bubbles form in the liquid and result in fizz.
Some people enjoy the fizzy sensation that comes from drinking a carbonated beverage. Carbonated beverages were once thought to be a kind of health tonic that could sooth an upset stomach.