As you fight you get more cards that you later use to unlock other rooms. The rooms you 'synthesize' have properties based on the cards you use, which is kinda cool. You end up making your own levels that way. Options include sleepy heartless, feeble heartless and never ending heartless swarms [which help you pick up cards].
In addition to ordinary rooms where you beat up on heartless there are 'story' rooms where you re-meet people from the first game from your memories of them. It's sort of like a 'season highlights' TV episode, where everyone sits around an reminisces about things that happened before -except exactly opposite because your memories don't remember you.