Diablo III's storyline takes place 20 years after the events in Diablo II, where a handful of heroes saved Sanctuary from demonic invasion thanks to their defeat of Baal, one of the three Prime Evils and the Lord of Destruction, and the destruction of the Worldstone (and with it Baal's armies).
Those events took place largely out of sight of the inhabitants of Sanctuary, and have since become stories of myth. Only Deckard Cain and a handful of other humans witnessed those events, and they are widely discredited and marginalised. Most of the inhabitants of Sanctuary therefore have a false sense of security, unaware of the danger posed by a potential demonic invasion and how truly perilous their very existence is.
Little is known of the core storyline of Diablo III at this point, though it is expected that the antagonists of the title will be Diablo, as well as two other major demons. One is known to be the Lesser Evil, Belial (the Lord of Lies), which makes Azmodan (the Lord of Sin) the other logical choice. Together they are the only Lesser or Prime Evils to not yet feature in a Diablo title. They also conspired with one another to successfully rebel against the Prime Evils (Mephisto, Diablo, and Baal) to seize control over hell, as explained in the original Diablo manual:
"In their ignorance, the Lesser Evils began to believe that the Three were afraid to continue the war with Heaven. Frustrated by the cessation of the war, Azmodan and Belial saw the situation as their chance to overthrow the Prime Evils and take control of Hell for themselves. The two demon lords made a pact with their minor brethren, assuring them that the wretched plague of humanity would not deter the ultimate victory of the sons of Hell.
Azmodan and Belial devised a plan to end the stalemate, achieve victory in the Sin War and ultimately ride the bloody crest of the Great Conflict straight into the very arms of Armageddon. Thus, a great revolution was set into motion as all of Hell went to war against the Three Brothers...
The Brothers fought with all of the savagery of the Underworld, and to their credit, annihilated a third of Hell’s treacherous legions. In the end, however, they were overcome by the Horned Death led by the traitors Azmodan and Belial. The Prime Evils, weakened and bodiless, were banished to the mortal realm where Azmodan hoped that they would remain trapped forever.
Azmodan believed that with the Three set loose upon humanity, the Angels would be forced to turn their focus upon on the mortal plane - thus leaving the Gates of Heaven abandoned and defenseless. Those few demons who still pledged allegiance to the Three Brothers fled the wrath of Azmodan and Belial, escaping to the realm of Man to seek out their lost Masters.
As the warfires died out upon the battlefields of Hell, Azmodan and Belial began to argue over which of them held the higher authority. The pact that they had made quickly fell to ashes as the two demon lords took up arms against each other. The legions of Hell that remained were polarized behind either warlord, launching themselves into a bloody civil war that has lasted to this day..."
Azmodan (Lord of Sin) art.