It's an odd thing to say Bungie's space epic has arrived and not mean the next title in the Halo franchise, but here we are. Destiny is Bungie's next big thing. Destiny is an always-online faux-MMO FPS. Players log in, join up with a small group of friends and save the universe one heavily structured mission at a time. In doing so, players will be rewarded with experience for their character, weapons and armor, as well as loot galore. Well, engrams for loot, which is really more like data which could turn into loot, but probably nothing worth... it's complicated.
You are a Guardian, raised from what should have been eternal peace to once again protect the Earth and the inhabitants that seek peace on it. Unfortunately, the battle has already been lost at least once. A powerful force known only as the Darkness eradicated the last vestiges of humanity once already, but through the power of a mysterious Moon-like being the Guardians will rise to fight once more.
Destiny features a full campaign, though admittedly there's more story to be found hidden in the lore than through standard narrative structure. The campaign serves to push players up to max level, whereupon they'll be tasked with acquiring more and more powerful armor. Eventually they'll reach a level of strength where they can take on the most challenging missions in Destiny, including weekly Strikes where enemies have been provided ridiculous strength or the lone 6-player raid which challenges players to work together unlike any FPS has done before.
Plus, Bungie is hard at work on multiple digital expansions to Destiny, if that's the kind of thing one goes in for.