When your child expresses her need to have her own space or room, this is an indication she is getting more independent and responsible. In her own space, she will try to find peace, calm, unwind and be alone with her thoughts and feelings. In short, having her own room will enable her to develop a sense of self-awareness. In the long run, she is getting mentally adjusted for adult life.
What you need to know
You want your child to be independent and develop her own identity. She knows her room is a place where she works on academics, reading or just playing an instrument. She studies, unwinds, thinks, experiments, finds her creativity in this sanctuary, that is her own room. Encourage this independence.