The Spectre is an ancient entity, created alongside his "brother," the Phantom Stranger, by a deity they call "the Voice." Their roles were meant to balance each other: while the Stranger was tasked with being the Voice's instrument of love, the Spectre was meant to be the mirror of the Voice's desire for justice.
The Spectre was first mentioned by the Phantom Stranger, who warned Pandora about the Spectre. (Justice League #6)
He first appeared when the Phantom Stranger sought him out, accusing the wraith of interfering with the Stranger's mortal family. The Spectre was found at a police precinct, in the office of Det. James Corrigan. The two had an instant hatred for one another; the Spectre blamed the Stranger for creating the circumstances of his damnation—to spend eternity as the embodiment of divine vengeance. Not much is known about the time of Corrigan's transformation. He mentioned that he loved a woman named Gwen, who died on the same night as Corrigan. The two demigods battled fiercely, but to no end; they were evenly matched. Ultimately, the Voice intervened and asserted that he created both of them, and absolved the Spectre in the matter of the Stranger's family. (Phantom Stranger #5)
When next he appeared, the Spectre was on the clock in pursuit of the notorious John Constantine. The Spectre was ready to reap Constantine's soul in payment for his many crimes against others. But as he often did, Constantine escaped his fate by convincing the Spectre that his current mission was actually in the Voice's interests. The Spectre was convinced and allowed Constantine to continue on his mission, but warned him that his reckoning could not be postponed forever. (Constantine #2)
James Robinson on the Spectre: "He’s not completely off limits, it’s just that for now, they have plans for him on the main Earth. … In my mind there is only one version of 'God' (for the whole DC Multiverse). … If there is one God, then there is only one Angel of Vengeance for God (which is the Spectre) so it makes sense that he would come to Earth-2 at some point. (Geekscape)
The Spectre's very presence causes instant paralyzing fear. As the "instrument" of an all-powerful deity, the Spectre's power is similarly limitless. He can warp reality to his whims and send souls on to their next state. His actions are tempered by the fact that he has a human host, one that sometimes provides the moral ground.