Coral is made up of limestone. The glue you use to make cement. But even so, coral gets broken off in violent tropical storms, drifts and can pile on top of other coral, just below the surface, to form a chain of islands, around a central atoll.
Eventually these tiny islands join together and a lagoon in the middle forms. This also fills up with coral cement (cay) and you get your coral island.
The Great Barrier Reef has a great number of coral Islands! 'Heron Island' is just one example of many others.