The Library Clan is one of the demon clans. Although it is not considered one of the major clans, it holds major importance to the story due to the characters who come from this clan.
As their name suggests, the Library Clan's members are able to access the Exterior Library, which cannot be entered by anyone else. There, they can see all of history and observe the outside world. Furthermore, the Exterior Library is an area of infinite magic.
Interestingly, the members of the Library Clan seem to lack any distinguishing physical features that might separate them from humans. Because of this, it is easy for them to integrate with humans.
Fourteen hundred years ago, the Library Clan moved to the human world and had descendants there. The Archbishop is a descendant of those demons, and it is likely that Female Magician is as well, since she is more closely affiliated with humans. Demon King and Senior Maid were either born before the Library Clan moved, or from members who either stayed in or returned to the demon world.
There are likely very few members of this clan, as only four are ever mentioned.