Sora and his comrades Goofy and Donald have been sent into a deep sleep somewhere in an undiscovered town, sent there by the witch Namine in order to regain the memories they had lost while in Castle Oblivion. In spite of that, all seems well... but the universe is left unattended, and thus vulnerable to affliction.
Somewhere, tucked away in a world few knew existed, an anonymous being followed in Ansem's footsteps. But, as opposed to studying the dark, their specimen was the light. Strange, white, almost humanoid creatures began to infest the land the researcher inhabits when the experiments started. Yet, the other people of the world seemed to find their source untraceable. Perhaps that is because the exotic creatures of light are not produced from experimentation after all...
The creatures that were produced seem to be much like Heartless, in that they take control of the hearts of other creatures—but instead of eating away at it, they swell it up with unhealthy quantities of light. The people of their world which had to experience it first soon knew what it was to have too much of a good thing. The white beasts, dubbed Lumens by their discoverers, overthrew the city and turned much of it's populace into mindless drones of perfection—essentially, one of their kind as well. Thus, their numbers easily expanded.
Once sick of the small world, they simply moved onto another (how the discoverer of the creatures remains unharmed has yet to be deciphered by anyone)—to a world called Basilica City. It is in comparison, absolutely immense in size, perfect for the Lumens to begin their feast once again.
All further information that is discovered of the Lumens is found via reports written by the discoverer. The reports are only accessed through special electronic journals which have been curiously distributed about the second world, Basilica City; some suspect it is also the discoverer's doings, perhaps a means to warn the people, yet no one is able to reveal why or how. All journals are able to communicate with one another through some sort of large network, so all journal users may discuss the situation at hand.
Worlds previously untouched seemed to be splitting at the seams, and the doors open once again. Strange things are happening—people every day are finding out that other versions of themselves exist somewhere else in the universe, that they are "Soul Sharers" as the locals have begun to call it. Currently, most souls seem to be sent to Basilica, the Lumens' new feeding grounds, with no recollection as to why or how they got there, acting as a beacon much like Traverse Town did in the past. Once again the universe is in complete shambles, but this time there is no one to save it.
Thus begins a one-sided battle against the very thing that was once sought to be preserved.
Extended information, of course, can be found in the userinfo of the game.