Dyus was the former keeper of the Great Library of Jyggalag as well as Jyggalag's trusted Chamberlain. Within the library, it listed formulaic predictions of the actions, events and deeds of all sentient lifeforms (creature, mortal and Daedra) in existence, that previously existed or is to be existing using the logical formula found within the library.
When Sheogorath appeared, he destroyed the library, seeing it as an abomination as he viewed that personal choice outlawed logical prediction. Sheogorath destroyed everything except for Dyus, seeing that he couldn't bring himself to destroy him due to the knowledge he possessed. So Sheogorath imprisoned Dyus inside Knifepoint Hollow and granted him immortality, making sure that he wouldn't die within his prison.
Haskill recommends that the Hero see Dyus at Knifepoint Hollow. Dyus will tell that the Eye of Ciirta and a branch from the Tree of Shades are needed. Once both items have been collected, return to Dyus. He will create the unfinished Staff. He then says to travel to the Tree of Madness in Sheogorath's throne room and tap the Tree's power to complete the staff.