Q2 was a member of the Q Continuum. At some point in the distant past, he misplaced the entire Deltived asteroid belt, an event which has caused him eternal embarrassment. He was later responsible for stripping Q of his powers and banishing him to mortality as a Human in 2366, having grown tired of constantly apologizing to lesser beings across the universe for the various misdeeds and trouble-making committed by Q.
Q2 continued to follow Human-Q's progress aboard the USS Enterprise-D. He later appeared and re-instated Human-Q's powers when the latter Q committed a selfless act to save the Enterprise-D from the attacking Calamarain, deciding that letting him die was not worth the trouble of explaining his actions to the Continuum. (TNG: "Deja Q")