There are many Blue Grottoes in the world, all of them are sea caves. Or more exact: caves partly filled with seawater with an entrance at or below sea level.
The reason for the name is always the same: the partly waterfilled cave has a connection to the sea. Sunlight entering the cave through the water gives the cave a mystic blue shine as the water filters the light and lets only the blueish components into the cave. The light shows all shades from emerald green to turquoise blue.
Most blue grottos are entered by boat. Sometimes you have to swim or dive to enter the cave. The Grotta Smeralda has a natural entrance deep below sea level, and is entered through an artificial entrance.