In antacids like Eno that fizz up when mixed in water, why is the citric acid important?
It's the citric acid that reacts with the sodium bicarbonate. When the tablet hits the water, the citric acid and bicarbonate react, forming $\ce{CO2}$ and sodium citrate. This causes the tablet to break up, thereby much speeding up its dissolution.

The table will contain a stoichiometric excess of bicarbonate, with respect to the citric acid, so it's anti-acid properties remain present, even after bubbling/dissolution. Dissolving a tablet that doesn't disintegrate due to the acid-base reaction and its fizz would take much longer.

The fizzing effect probably also has some aesthetic/marketing value, separate from anti-acid properties of the tablet.