Improves upon the original in nearly every way.
The story takes place 1 year after Chain of Memories (CoM) and you begin playing as Roxas, a 15-year old boy who lives in Twilight Town. Sounds like it has nothing to do with Kingdom Hearts but as the story moves on you find out that Roxas is the 13th member of Organization XIII, the antagonists of CoM. Axel, one of the villains of CoM is later revealed to be Roxas' best friend and Roxas is revealed to have been kidnapped and placed in a fake town and his memories erased by DiZ, another mysterious character from CoM. Roxas then regains some of his memories, finds Sora, who is still sleeping in the same pod as in CoM, and then fuses himself with him, much to Axel's dismay. Sora, Donald and Goofy wake up from they're long sleep and set out for another adventure to stop the villanous Organization XIII and they're mysterious leader from gaining the heart of all worlds. (Confusing? i'm not surprised).
The gameplay is now less of a hack-and-slash combat and instead you have cool and smooth combos and powerful and awesome combo finishers. You can also use Drive Forms this time around which allows Sora to carry two keyblades and gain useful abilities when you level up you're drive forms. You still have summons that are all classical Disney characters and magic to help you in battle. The magic is also much better and much more powerful this time around and works much smoother.
The game also has a great replay value. After you finish the game you still have 4 normal tournaments to finish and 4 secret tournaments. Multiple mini-games can be found in different worlds and getting a high-score for them will complete Jiminy's Journal. You can still fully level up normally and fully level up you're Drive Forms and summons. There is also a secret ending if you finish certain things. Those things differ from the difficulty you choose when you play the game.
Overall, Kingdom Hearts II is a great game and a great improvement over it's fantastic predecessor. If you're a fan of Acton RPG's get this game at all costs.