She gave herself the name "Biwa" after the instrument by that same name. Her father was a biwa player, and her mother was a shirabyōshi (female entertainer). The biwa, which she carries with her, is a memento of her deceased father.
Biwa is an unusual character for an anime. She is not the protagonist, who determines the flow of the story. She is the sky, who watches the events as they unfold in front of her eyes.
She can see the future using her right eye, but she refuses to tell others what she saw. In the beginning, she does it out of spite, because she holds a grudge for the death of her father. However, in later episodes she does it out of understanding that the future cannot be changed.