Stony corals build their skeletons as cups called corallites, one per polyp. In most species each cup is discrete. In meandroid corals such as Diploria labyrinthiformis, polyp division proceeds without the daughters fully separating, so the corallite walls run together into long sinuous valleys with the mouths lined up inside them.
The ridges between valleys are the shared skeletal walls, and in this species a groove runs along the top of each ridge, which is the feature the common name records. Living tissue covers the whole surface and is continuous across the colony, so nutrients captured by one region can move to another.
Growth is slow. Radial extension for massive Caribbean brain corals is generally on the order of a few millimetres per year, so a boulder a metre across represents a long span of undisturbed reef. The frequent misconception is that a large brain coral is a single old animal. It is a colony, and the tissue is a connected sheet of many small polyps rather than one large one.