Nodes were machines used as interfaces to the central computer of The Library.
They had limited functionality, answering visitors' simple questions and passing on messages. Each was like an abstract statue, with a large headpiece which contained a "real looking flesh aspect", a human face. Such faces were donated by people who had died, a practice apparently quite common in the 51st century. One of the people who had donated a face was Mark Chambers.
Faces were chosen for each user individually from flesh banks by the computer, based on what it thought the user would like.
It was from such a node (with the name 710/aqua) that the Tenth Doctor and Donna got their first clues to what had happened in the Library, as it replayed a message by the head librarian, warning visitors to count the shadows.
Donna briefly became a node when the Doctor failed to send her back to the TARDIS. (DW: Silence in the Library / Forest of the Dead)
In the Doctor Who Experience there is a Node in the Starship UK museum, suggesting that Nodes were in operation prior to the 29th century.