They are an order of Monks (or whatever the gender-neutral term for monk/nun is) dedicated to Julianos. Given the heavy metaphysical nature of the Elder Scrolls, I think the term Priest might be appropriate. As for their history, not much is known.
Finally, I believe that there were oblique references back in daggerfall to the Cult of the Ancestor Moth, though they most definitely were there by Morrowind.