Neverland is a world based on the 1953 Disney movie Peter Pan. Despite the world's name, you don't actually get to go to the islands of Neverland. Instead, most of the world is spent on Captain Hook's ship.
When taking the Gummi Ship route to Neverland, the Gummi Ship will come across what looks like a pirate ship. After a long cutscene where Sora is once again reunited with Riku, the party ends up in the Ship Hold. After another cutscene, you'll be able to add Peter Pan to your party. Your new mission will be to find Wendy and Kairi. Exit the area through the door to bump into Shadow Sora, the Heartless Riku introduced earlier. After he leaves, climb up the ladder and enter the door on your right. Go down the ladder here to enter another short battle with Shadow Sora. Now exit the Freezer by climbing up the ladder for a long cutscene. The party locates Wendy and Kairi only for them to be taken away shortly after their arrival. Go through the door and, once again, battle Shadow Sora. Go through the door next to the ladder for another battle with Shadow Sora. Jump up on the shelf to reach the roof above. Where the net is torn you'll be able to jump up to the next floor. Make sure to jump through the opening on the right. In this room, make sure you have Sora, Donald, and Goofy in your party, since you'll need to activate the Trinity mark. Climb up the ladder that's brought down for a cutscene. Sora didn't seem to make it in time, as Riku is leaving with Kairi. He summons an AntiSora Heartless, which serves as your next boss.
After the battle, go to where AntiSora disappeared into the ground and Examine a section of the floor. Here will be a trap door, which you can drop through for a cutscene. At this point, Peter Pan will leave your party to help Wendy. The rest is up to Donald, Goofy, and Sora. Exit through the door and then go through the door on the right to end up in the place you were before the battle with AntiSora. Climb up the ladder and exit through the door in front of the trap door for a cutscene.
After the cutscene, Peter Pan will return as an optional party member and Sora will have the ability to fly. Sora also gains information on the whereabouts of Riku - Captain Hook tells Sora that Riku went to Hollow Bastion in search of Maleficent and, unfortunately for Sora, he took Kairi with him. After the cutscene, you'll have to defeat the Heartless left to you by Smee and Captain Hook. The controls for flying are the same as swimming - to ascend and to descend. After you get used to flying and finish the battle with the Heartless, a cutscene will show Captain Hook coming out of the cabin to fight the party.
After the battle and another cutscene, you'll end up on London's clock tower, Big Ben. Here, all of the clock's hands will be set to 12:00 except for one, which is 12:45. Hit the hands with the Keyblade to make it 12:00, and the Keyhole will be revealed. Afterward, you'll gain a new summon, Tinker Bell, and you'll be free to leave the world.