Great Improvement in Gameplay and Graphics!
If you've played and finished the first Kingdom Hearts, you'll notice that there is a slight gap between the beginning of Kingdom Hearts II to the ending of Kingdom Hearts. Though it was slightly explained in the introduction of Kingdom Hearts II. They said the story gap can be played in Kingdom Hearts: Chain of Memories which is for Gameboy Advance.
After a long Introduction (about 3-4 hours or more). Sora continues his search for his lost friends, Kairi and Riku. Just when he thought that he cleared the worlds of the heartless, he now encounters more than the heartless, and discovers the nobodies, and finally meet the Organization XIII.
Kingdom Hearts II comes with a new feature called the Drive Gauge which you use to Summon Allies and Transform into Drive forms, which have different specialties and are leveled up separately, while Summons do level up with continues use.
The Gummi Ship is now more enjoyable and unlike the Gummi Ship in the First Kingdom Hearts which i really didn't like, because of being complicated and all. Now it is much much better in a lot of ways, which have a better control, and good levels.
The Graphics are pretty much improved character and world details and comes with a fix on the camera angles.
The Gameplay is an improvement of the hack-and-slash system with more combinations of attacks, and the drive gauge adds to it big time.
The Theme Song is done by Utada Hikaru (Sanctuary), which was pretty well done.
There are a lot of side quests you can do, Sephiroth (Final Fantasy 7) is back. (He was also in KH1) who is an optional boss (A tough one), Coliseum Tournaments, Gummi Ships.
By the way, Setzer Gabbiani from Final Fantasy VI makes an appearance here. Just letting you know if you ever were interested to see him in full 3D. :D
OVERALL:
A great improvement in Gameplay and Graphics, Great continuation of Kingdom Hearts and Kingdom Hearts: Chain of Memories.