Why is carbon dioxide added to fizzy drink?

To make it 'fizz'.

Carbon dioxide is dissolved in water , under pressure.

It is kept under pressure.

When you open the can/bottle you are releasing the pressure, hence the carbon dioxide 'fizzes' out.

NB

Many gases can be dissolved in water, and kept under pressure. Whilst under pressure, the gas is held in solution. and you don't see any bubbles.

The moment you release the pressure, the gas held in solution comes out 'Fizzes'.

A similar event is water boils at a lower temperature, when the pressure above it is reduced. Boiling water is the release of gas held in solution.

The hotter the water or the lower pressure, then less gas is held in solution.

Conversely for higher pressures and lower temperatures.