A half-world is a plane of existence that has not yet been (and may never be) fully realized. They might someday become full alternate realities, but as now they're merely half-worlds, similar to demiplanes in the sense that they're finite. Unlike standard demiplanes, half-worlds don't exist within the Ethereal Plane. Unlike Fading Lands, they aren't coexistent with the Prime Material Plane, either.
The adventure Dead Gods introduced a half-world known as Naphraks. "Naphraks is one of the small domains known by a select few cutters as half-worlds—special demiplanes accessible only by traveling the World Ash. Many half-worlds are unoccupied, while others are used as secret layers, refuges, lairs, and even prisons. Some graybeards think that Yggdrasil itself (or herself, as the ratatosk say) creates the half-worlds. 'Course, a lot of these same bashers claim the tree spawned all of the planes like fruit."
Half-worlds of Tovag Baragu
In the adventure Die Vecna Die!, Vecna's meddling with the very shape of the multiverse in the otherworldly city of Sigil created changes to the structure of the planes that could not be erased. One of those changes was the creation of half-worlds, both in the present and the recent past. Around 591 CY, before Vecna's meddling actually began, many half-worlds formed around the interdimensional structure known as Tovag Baragu, many of them resembling versions of Oerth in which history had happened differently, though with no existence outside of a small bubble around the local form the stone circles of Tovag Baragu took.
The concept of unfinished alternate realities occurs elsewhere in Bruce R. Cordell's work. Dawn of the Overmind, the third adventure in his illithid trilogy, features a "stillborn multiverse" that represents an alternate reality where the illithid empire never fell. Because it's a stillborn multiverse and not a born one, it may be safe to assume it's not an infinite expanse of parallel realities, but something more like the half-worlds of Tovag Baragu, unfinished. As with Tovag Baragu's half-worlds, it never fully came into being. The illithids mean to change that.
After the events of Die Vecna Die!
After Vecna was cast from Sigil, the half-worlds are said to "multiply a millionfold, taking on parallel realism in what was before a unified Prime Material Plane. The concept of alternate dimensions rears its metaphorical head, but doesn't yet solidify, and perhaps it never will."
- Bulmahn, Jason, James Jacobs, and Erik Mona. Expedition to the Ruins of Greyhawk. Renton, WA: Wizards of the Coast, 2007.
- Cordell, Bruce R. Dawn of the Overmind. Renton, WA: Wizards of the Coast, 1998.