According to their legends, this Q was a formless entity (referred to by the male 'he' or the neutral 'it'), hungry and chaotic, that once walked among the people of the mirror universe, and conquered many races. When he set out to conquer Terrans, however, they found some secret weapon against him, perhaps an ally of god-like powers or an ancient magical incantation, and banished Q to a prison outside the known dimensions.
From this place, Q was only able to communicate with his chosen people, the Orions, and only through certain religious ceremonies. It was Q's command that they spread suffering, confusion and fear. The Cabal's ultimate goal was to free Q, so he could then lay waste to the known Galaxy, punish the Terrans, and finally alter the laws of physics to elevate his loyal servants into powerful beings like himself, and together they could rule the fractured reality.
However, beyond the claims of the Cabal priests, the Q Continuum was not otherwise known to exist in the mirror universe, or they hadn't revealed themselves to anyone else there. (Decipher RPG module: Through a Glass, Darkly)