What exactly did the Roman senate actually do during the Imperial Era? Were they just some kind of glorified debate club with special privileges attached to it? Were they like advisors to the emperor or something? Were they still elected or did the emperor just appoint whoever he wanted?
They provided a veneer of legitimacy and legality to the Emperor's imperial orders. At least under Augustus and the first Emperors they conducted business much as usual except their decisions were a formality, a 'rubber stamp' for the Emperor's wishes and they operated only with his express blessing (knowing full well which hand they fed from)