Profile
The Girl is the first character to appear in DW: Silence in the Library. She is on Earth, describing to Dr Moon (an apparent psychiatrist) a world that she sees when she closes her eyes; a world that is later shown to be The Library.
In the world of The Library, the Girl is seen as a floating metal sphere that turns off and falls to the floor when the Girl opens her eyes on Earth. While The Doctor and Donna Noble were in the Library, they came across this metal sphere, which the Doctor identified as being a security camera, although he told Donna after examining it that it was indeed alive.
The Girl came into contact with the Doctor through her television screen, where they engaged in a brief conversation which was ended when the technology malfunctioned.
Shortly after this encounter with the Doctor, Dr Moon came to have a talk with the Girl alone. Here, he told her that there were differences between the Real World, and the World of Nightmares. When the Little Girl said that she already knew this, Dr Moon shocked her by telling her that the Real World was false, and the World of Nightmares was real. He told the Girl that the people inside 'her' Library were very real, and that they needed her help.
The Little Girl then proceeded to 'save' Donna Noble, possibly killing the Doctor's companion in the process. The Girl turned to her father shortly after, telling him that "Donna Noble has been saved." It is unknown at the present time whether Donna Noble is alive, or dead. DW: Silence in the Library/ Forest of the Dead
Behind the Scenes
There is speculation throughout the fandom of Doctor Who that the Little Girl is the centre of the Library - the super computer that controls the planet.
It is also speculated that the Little Girl is what the archaeologists in the Library called CAL.