It seems that things aren't quite as settled as everyone thought -- Heartless are popping back up in places and making a right nuisance of themselves all over again. While there are not nearly as many as there once were, their numbers are growing, and the Restoration Crew are finding it a bit too hard to take care of them themselves. They have other things to do, after all, like rebuilding their homes and getting on with their lives, and, as always, there are not enough hours in the day to take care of everything.
After receiving a letter from King Mickey requesting their help, Sora, Riku, and Kairi packed their bags and headed to Radiant Garden, curious as to why things seemed to be starting all over again. Surely there was a reason for it, but with no villains in dark cloaks running around and harassing Sora, they found themselves faced with two probabilities: one, that the heartless were still spawning on their own from some unknown source, or two, there was a new megalomaniacal bad guy around, controlling the heartless and biding his time to make attempt number three at destroying the universe via use of heartless. Neither idea was particularly appealing, and it was decided that, once again, it would be up to Sora and his friends to fix things.
On top of all of that, it seems that, unbeknownst to out intrepid heroes, the members of Organization XIII are back, though in their original bodies. They have no memories of ever being in the Organization, and, for all intents and purposes, are back to living their normal lives -- until they, too, get mixed up in the business of dealing with the heartless.
The game picks up about a month after our intrepid trio arrived back at Radiant Garden. They're no closer to discovering the new source of heartless, but they're slowly clearing up the worlds again and helping the Restoration Committee. It's slow and sometimes frustrating work, but they're determined to clear things up (for the final time) so everyone can get on with their lives.