Bungie has a way with expansive worlds and fiction--just look at the Halo series. So we expected the same from Destiny, and the company has started to show its hand, sharing more details on the world, story, and the three classes.
The official site shares the details. The white orb, called the Traveler, ushered in a golden age for humanity. After expanding throughout the solar system, humans were pushed back by some malevolent force. All that's left now is a single city (simply called "the City") under the shielding of the Traveler.
You'll play as one of three classes, Guardians of the City: Warlocks, Titans, and Hunters. Warlocks tap energy from the Traveler itself, Titans seem like strong brutes, and Hunters are a bit more lean and quick.
Finally, a few of the environments and enemies are outlined. The earth is an overgrown wasteland, the moon is forbidden, and Mars and Venus are both so remote that they're out-of-touch. Enemies come in two flavors, the Fallen and Cabal. The Fallen have a few classes of their own, and seem like an organized group of human scavengers. Cabal are more mysterious, and the site implies that they haven't been seen in quite a while--which probably means they're the more serious threat.