Yuri hides herself whenever her father has any visitors, due to her horribly burned face (she barely looks human). The fire also took her voice, so that she is unable to communicate except by telepathy or by some visual method. The only people her telepathy "speech" reaches are Yumi, Lan, and Wataru (although she could probably communicate with Sonnet, had they anything to say to each other. As a matter of fact, there is a possibility that Sonnet did communicate with her at the end of OVA #3).
She was once the pride of her father's research, and then ran off with a young man and became pregnant. Her father tracked her down (it is unclear whether this were before or after Yumi's birth) and told her lover that she was a telepath, emphasizing that this meant that she could read his mind and see whatever he wanted to hide. The man left her, and Yuri hit her father over the head and threw herself into a fire. They were rescued by her father's research assistant, and since then Yuri has buried herself at the Onagara house in the mountains until she is again drawn out, both by Lan's need and by Talon's cruelty.
It seems that what Yuri wants most is to walk among other people and be accepted as one of them. When Bird gets her a mask and wig, she is delighted. (She looks very pretty in her disguise, as well.)
Yuri's "voice" is done by Shinohara Emi, of SailorMoon, Project A-ko, and Kekko Kamen fame.