The Klay Disks are small items that can be picked up, and seem to represent compund discs. They are played in Disk Players.
Each disk holds a part of a story told by Willie, called "The closing of the Third Age".
The story is about when Hoborg created the Neverhood. Over time, Hoborg felt alone in his world, so he created Klogg from one of his Life Seeds. Klogg then seemed to represent Klaymen (yet he only had one button on his chest, and assumingly, was white and brown). Hoborg told Klogg to explore his world and enjoy himself, but soon Klogg started scheming to steal Hoborg's crown.
As Hoborg was sitting on his throne, wondering what to call his next son, Klogg stole his crown. He put it on his head and because of the crown's powers he turns into the form he is in the game, while Hoborg, who needs his crown to live, falls into a deep sleep.
Willie saw it happen and was concerned about it. However, another life seed Hoborg was holding jumped out of his hand, and Willie took it and threw it into the Nursery. Klaymen was born then.