The Cave of the Gi is a location that you can reach from inside Cosmo Canyon. Bugenhagen takes your team in to the Cave (where you must have Ninaki/Red XIII in your party) in order to have Red XIII learn more about his past.
The story of the game leads the team to Cosmo Canyon after they have left the Corel Prison and have traveled through Gongaga. The Cave of the Gi is a non-optional area that you must complete while in Cosmo Canyon. Check out the Cosmo Canyon walkthrough page for more details on how to navigate this dungeon.
There are a number of items that you can pick up in this area and there is no way to re-enter the Cave of the Gi later on in the game, so make sure you grab them all:
Added Effect Materia
Black M-phone
Ether
X-Potion
Turbo Ether
Fairy Ring
Gravity Materia
The map below shows the location of the Cosmo Canyon (which is where you can find the Cave of the Gi) on the World Map:
