Rhun was the name Gondorians gave to all of the land east of the Sea of Rhun, so would have been home to the Easterling tribes which had invaded the West on occasions (the Wainriders etc). Not much is said about these lands, but in the appendices it does mention that Aragorn and Eomer fought wars there before they could have peace. The two blue wizards, Pallando and Alatar were said to have gone into the East too, but nothing more is known of their fate.
And was Saruman really bad when that happened? Wasn't he just a little jealous of Gandalf and that was it?
but I'm not sure if that's exactly true though about Saruman being jealous, IDK. Could have been anything.