The Gym is one of the many rooms in Lara's Home in Tomb Raider III. It serves as a training area that introduces the player to Lara's moves, like jumping, sprinting, crawling and monkey swinging.
When entering the Gym, Lara advices the player to do the excercises in order. The different platforms and excercises are marked in numbers from one to eight. At each excercise Lara tells the player how to do the move.
After getting to know Lara's moves, or if one already knows them, testing out one's skills at the Assault Course might be a good option.
The Pool House is in the next room accessed via the Gym.