Aggamon's true origins are unknown. He may be a native of the Purple Dimension, or he may just have set it up as his own base. He commented, "In a thousand years, no captive has ever escaped through the Purple Veil!"—which may indicate that he has ruled there for a millennia.
At some point, he began to bring natives of other dimensions to the Purple Dimension, and turned them into slaves, to mine the gems of that dimension. He trades the gems to others in exchange for power for himself.
Two men stole the Purple Gem from Dr. Strange's Sanctum, and were pulled through the gem across the Purple Veil, where the were enslaved by Aggamon. Strange traveled to the Purple Dimension in order to free the two men. Aggamon agreed to return them to Earth, if Strange would take their place as prisoner. Dr. Strange agreed, but after the two men were released, he explained he only agreed to take their place, and not to stay there. Freeing himself, Strange challenged Aggamon to single combat. Aggamon used his Jeweled Demolisher Beam against Strange's amulet. The two locked in power for hours, and their very life forces began to weaken as they focused all of their power against each other. Ultimately, it was Aggamon who lost the game of "Chicken," surrendering to Strange rather than risking death. Before leaving, Strange cast a spell over Aggamon, weakening him, and telling him that he could only ever regain his strength by releasing his slaves.
Aggamon was one of the "Lords of the Nether-Worlds," summoned to the Dark Dimension by Dormammu to observe his battle against Dr. Strange (as later revealed in Dr. Strange: Sorcerer Supreme Annual#2/5). The Lords returned to their respective realms after Dormammu's defeat at Strange's hands.
Dr. Strange was attacked by the Minions of Mordo: Adria, Demonicus, and Kaecilius. As Strange began to overpower the three, Adria located the Purple Gem. Sensing its power, she tried to use it against Strange. However, the Gem served only as a one-way portal to the Purple Dimension, and all three of the minions were sucked away.
Clea and Flyx (actually Dormammu in disguise) sought allies against Umar and Baron Mordo. They began their quest to recruit the Lords of the Nether-Worlds with Aggamon. The lord of the Purple Dimension declined, explaining that he must remain neutral in order to maintain his trade of the Purple Gems. He then offered to sell them a gem, saying that they might use it to court the favor of one of his fellow "Lords." Clea and Flyx agreed, but he then entrapped them within the Purple Gem, as punishment for his past defeat by Strange. However, they managed to escape: Flyx called upon his "full Faltinian power"—maintaining his cover-up as Dormammu—and shattered half of Aggamon's domain. They then bluffed Aggamon ("Flyx" had exhausted his stored power) into surrendering, and they agreed to leave them in peace if he would supply them with all of the gems of power they need for the upcoming conflict with Umar.
Clea and Flyx (presumably utilizing the power of the Purple Gems), alongside Tiboro and five other Sorcerers (whom I can't identify, presumably other Lords of the Netherworlds), traveled to the Dark Dimension to take down Umar and Mordo. They were successful, and Umar conceded defeat and relinquished the throne rather than face the combined power of the sorcerers. However, Flyx than revealed himself as Dormammu, retook his power, and banished Tiboro and the others from the Dark Dimension.