Final answer:
The narrator believes her room was initially a nursery and later used as a playroom and gymnasium, evidenced by the safety bars on windows and exercise fixtures on the walls.
Step-by-step explanation:
The narrator believes that her room was once a nursery. She describes the room as a big, airy space that was used first as a nursery and then as a playroom and gymnasium. This interpretation is based on the fact that the windows are barred, which is typical for a child's safety, and there are rings and things in the walls, suggesting that the room was equipped for children's activities and exercise.