The Great Lunar Cataclysm was a disaster that took place in the year 2037 of the 2002 Film Timeline. It devastated the Earth, leading to Humanity's degeneration into Eloi and Morlocks. ("The Time Machine")
As of 2037, Humanity had been mining from the moon for decades. Unfortunately, they had over-mined the moon by 2037, causing it to drift out of its orbit colliding with the earth's atmosphere, tearing the moon apart and sending debris crashing to Earth. The moon's destruction shifted the orbit between the moon and Earth, devastating the cities on the planet. Luckily, most of the moon stayed intact, while some remained in Earth's orbit, forming a ring around the planet.
It was one of the most devastating disasters in the history of planet Earth. Its cause was said to be the fault of demolition work within the lunar surface; preparing it for the future expansion of more subterranean homes. Unfortunately this shattered the moon, de-aligning its orbit. The combination of the demolition work and the power of the Earth's gravity caused the moon to shatter. This scene in the movie is portrayed as foreshadowing the eventual degeneration of the human race into the Eloi and Morlock.
Because of this cataclysmic event, the Earth would lie in ruins for thousands of years. Sand storms raged across the landscape, killing most of the earth's species while signs of human civilization - cities, buildings, vehicles, were buried. Time took it's toll on the land, where there was once luscious green, the sand wiped it away. However, the Earth began to heal itself about 100,000 years after the great cataclysm. Amazingly, the Earth became fertile once more; grasslands and forests re-appeared on each of the continents. By 400,000 A.D a new ice age had risen, with snowstorms and glaciers dominating the northern hemisphere. Eventually, the ice age decline after many centuries and the Earth became a tropical paradise. By 802,701 most of North America was covered in rain forest and the world had now fully recovered and Humanity had split into two subspecies, one returned to a primitive lifestyle while the other survived underground. As for the moon, it remained in ruin, but its remnants continued to orbit the Earth.
[Edit: In actual fact, the gravity of the moon would have a far greater impact on the fragments, than any gravity exerted by the earth, and so even if humans had managed to destroy the moon, breaking it into fragments, those fragments would have remained together, coalescing into what would functionally be a single object, once again. In other words, the moon may have exploded, but its gravity would have drawn all the moon-bits back together again, reforming itself into the moon once again. There simply aren't enough shearing forces acting on the moon to override the gravity of the moon itself, so the fragments will never disperse, as shown in the film.]