Adron's Disaster was the culmination of several events, most of them described in Five Hundred Years After. The basic facts of the disaster are that Adron e'Kieron attempted to claim the Orb from Emperor Tortaalik using Elder Sorcery and, simultaneously, Mario killed Tortaalik, in the process making Adron the new emperor
Adron lost control of the amorphia which powered his spell, and it devoured Dragaera City and all its inhabitants. The Lesser Sea of Chaos (composed of amorphia) now occupies the area around the site of the disaster. Thanks to the efforts of Sethra Lavode (who was with the emperor when he was killed), the Orb itself was saved. Sethra succeeded in teleporting it to the Paths of the Dead before it could be consumed by the explosion. Adron's daughter Aliera was disembodied but not killed, thanks to Sethra's intervention at the time.
The effects of the disaster were not confined to the immediate area around Dragaera City, however. There are stories of massive earthquakes all across the Empire, and huge "breakwaves" in coastal areas. The failure of sorcery consequent with the banishment of the Orb to the Paths of the Dead also resulted in numerous secondary disasters, including the destruction of various floating castles in the countryside and above some cities, and the collapse of Kieron's Watch into the sea.
The result of the Disaster was instant disintegration of the Empire, loss of the Orb, and an Interregnum lasting 247 years.
Some sources have argued that the second Dragon-Jhereg War played a role in the disaster, by causing Adron to act against Tortaalik sooner and with fewer resources than he would have preferred. Others, including Paarfi, discount the significance of this event on the actual disaster.
Why Adron is often blamed as the sole cause of the disaster in many Dragaeran's minds, we don't know. It was nearly as much Mario's fault as Adron's, yet he is rarely mentioned. This is partly because Adron, upon losing control of the amorphia, said to Khaavren (in Five Hundred Years After) "Don't tell them that I meant well".
Some say that Adron's consciousness survived the disaster and lingers in the area of the Lesser Sea, perhaps still exerting some influence over the amorphia there.