This world is a Disney World designed from the movie Aladdin. This world is special and makes appearances in every Kingdom Hearts game (except Birth By Sleep) up to this point.

In KH1, it serves as the more plot-changing world, where Sora finally first learns the Disney villains' scheme, or at least, learns who Maleficent could possibly be, and also realizes that the princesses are starting to be kidnapped, having failed to understand why Alice vanished in Wonderland. Sora is used in this world as the helper, like many other worlds. Sora fights alongside Aladdin, helping him capture Jafar and save the world. After completing this world, you get the Genie Summon. Also, this world plays host to one of the most fun bosses in the whole game. Kurt Zisa. After returning, talk to Carpet in Aladdin's house, he'll take you to the fight.

This world also takes on the basic plotline of the movie Aladdin.

 

In KH CoM, this world was used as a point of telling people that caring for the people you cherish most is more powerful than any force in the world, and the memories of them can only make you stronger. Sora passes through with that lesson in mind, gaining items, Keyblades and the Genie summon at the end.

 

In KH2, this Disney World is featured once again, and plays out similarly to that of Aladdin 2, The Revenge of Jafar. However, the plot is much broader, and areas have all been altered from the first KH game. The only area that remained the same was the entrance to the Cave of Wonders, being open since the last visit.

Sora is used in this world this time simply to play alongside the original plot, occasionally stepping in to help out. You obtain the Genie summon after completing this world the first time. (I think)

 

In KH 358/2 Days, Roxas visits this world as more of a side thing. The details of this world are unimportant to him, but the big thing is that he first is introduced to Pete here, and is wondering who he is. Also, Roxas passed out in this world just after he completed one of his missions, and wasn't well since.

Roxas is used in this world as the miracle to Aladdin and Jasmine's plans to rebuild Agrabah to be peaceful and Heartless-free once more. He makes contact with the people in this world however, by having a nice chat with Genie and the Magic Carpet, even if he was confused at the moment.

Notice how this is the only world where the Keyhole is featured as a room, just unenterable at the moment. You can never actually enter the Keyhole, they just put the black line on the map to show it's a possible area.

This is one of the areas used in the Xion fight. She takes a similar form to Kurt Zisa from KH1.