At the end of Diablo 2 Baal destroys the Worldstone, but I'm really hazy on the purpose of the 'World Stone'. Are there any official explanations, in a novel or statement by blizzard what the stone's destruction did to Sanctuary? How does this lead into the story of the next game?
Executive Summary: The destruction of the Worldstone had devastating physical effects to the Arreat Summit's immediate surrounds - turning it into a massive crater and poisoning the land. But it had a more interesting effect: with the Worldstone no longer actively reducing humankind's powers, they are reverting to nephalem with the associated powers that they once held.
The purpose of the Worldstone was two-fold.
The first is revealed in the novel, The Veiled Prophet. The Worldstone was the foundation for Sanctuary, as it was used to create it:
he cannot be touched, for he’s tied to the very foundation of Sanctuary, the Worldstone!
Distance had no meaning where the Worldstone was concerned. Though it physically appeared to be hundreds of miles away, it was, in truth, everywhere.
Tyreal makes reference to this in Diablo III as well:
Since time immemorial, the forces of Heaven and Hell fought for control of the sacred Worldstone... until the day it was stolen by renegades and used to forge your world.
The Book of Cain also touches on it:
Inarius succeeded in manipulating the power of the stone to create the world of Sanctuary.
The second use came later, when it was changed to restrict the powers of the nephalem to reduce them into mere mankind:
Tyrael: To escape the Eternal Conflict, a group of renegade angels and demons came together and created a hidden paradise for themselves. They called this world Sanctuary.
Eventually, they commingled. They gave birth to mankind. That is why you have both good and evil within you... and the power of both realms as your birthright.
The power of your nephalem ancestors was so terrifying to their parents that they tuned the Worldstone to weaken them. They knew they had loosed something... unimaginable upon creation.
Deckard Cain: The Worldstone was an ancient artifact of immense power. It was used not only to create our world, but also to control mankind.
The original humans were known as the nephalem, and their power was such that it was feared they would tip the balance in the Eternal Conflict between the High Heavens and the Burning Hells.
So the Worldstone was tuned to lessen our powers, turning mankind into what we are today.
And from the Book of Cain:
Inarius then attuned the Worldstone to cause the powers of the nephalem to diminish over time.
Destroying the Worldstone could have effects on either of these purposes. Obviously it did not destroy Sanctuary as could have been reasonably expected, and equally obviously it did have a physical effect - it created the Arreat Crater where Azmodan has set up his base:
Deckard Cain: Tyrael was forced to destroy the Worldstone when Baal, the Lord of Destruction, corrupted it in his attempt to control all of mankind. ... It obliterated Mount Arreat, the mountain that housed it, leaving only a smoking crater in its place.
The Book of Cain:
the surrounding area was devastated. To this day, toxic clouds of ash and choking arcane dust hang like a shroud over the land. The decimation was so utterly calamitous that this region is now known as the Dreadlands.
However there is reason to believe destroying it did affect the weakening of the mankind, restoring them to their status as nephalem:
Deckard Cain: So the Worldstone was tuned to lessen our powers, turning mankind into what we are today. But now that it has been destroyed, it is conceivable that the powers of the nephalem will reappear.
This become explicit throughout Diablo III as the remaining Evils, Belial and Azmodan, as well as the Angels encountered in the Heavens all repeatedly refer to the player character as "nephelam", implying that they also believe that humans are regrowing to the powers initially possessed by their nephelam ancestors.