This is an enclosed gym with a round arena, where you can exercise before you take your bath. Your slave is going to rub your body with the perfumed oil he carries in a small flask. Now you are ready to start your routine with a good warm-up.
This photo is actually from an open arena at Pozzuoli, but its shape and amphitheatrical seating give you an idea of the arrangement in the Baths of Trajan. (Navigation aid: layout of the virtual Baths of Trajan)
Apodyterium A