The Deep Sea Research Center is a large complex out in the middle of the ocean, which was used to conduct various research and experiments regarding the sea and it's creatures. In Final Fantasy VIII, it is found to have been abandoned, for what seems like a long time.
The Deep Sea Research Center is an entirely optional location in Final Fantasy VIII. All enemies, bosses, and GFs available aren't necessary for the story. The Deep Sea Research Center goes down 100 floors, starting with a large open room containing the legendary dragon GF, Bahamut. The bottom floor is the secret super boss, Ultima Weapon. It has the strongest, final GF, called Eden, available to the character. This fight is considered a way to show off the skill of your team, as well as give great rewards to your party.