The Uncommon Room is a comfort and a refuge for the Faculty at Unseen University. Those members of staff who still haven't been able to shake off those last few residual teaching duties would far rather be here than in Rooms 3b or 5b taking classes. Happily the nature of the University is frequently able to oblige them on this.
Here, plots are hatched, crisis meetings take place whenever the Fabric of Reality is about to be rent asunder by the Pool-Cue of Scientific Inquiry, and there are many comfy chairs where sherry may be consumed and bickering may take place among some of the Discworld's most finely-honed minds.
For those who are unaware, one of the eccentricities of British academic life is that, in the more uppity public schools such as Eton or Winchester, or at least at the older universities such as Oxbridge, calling the rest-room for the employed teaching staff a "staffroom" or a "staff lounge" is frightfully common and vulgar. It might do for the sort of comprehensive school down the road or at The University of The North Circular Road (formerly Neasden Polytechnic) where there aren't any traditions, but here, it's the Masters' Common Room, or the Senior Common Room, you unspeakable little oik.
At Unseen University, what better for the unique and singular staff members than an Uncommon Room?