I used to be a scuba diver, including diving in tropical oceans, so I'm familiar with what you found. I've got several immature (small) examples of it, as souvenirs I found on diving trips to the Caribbean. Here's your answer about brain coral.
"Brain" coral is the nickname given to that particular species of coral for two reasons:
1- When that species grows to its massive (several feet wide) fully-mature size, its form is an oval-shaped rounded-top dome, like a brain.
2- The curving ridges/channels across its surface make it very closely resemble the surface of the human brain.