The actual animal that makes up the physical coral is called a polyp. It is column shaped and attaches itself to the floor of the reef. The top end extends into the water and is free to move about. Thousands of individual polyps form a colony, which in turn forms a reef. Each individual polyp is responsible for each bump in the reef.
Polyps are active at night.
During the daytime, they retreat into their skeleton, so divers usually only see their skeletons.