Maxwell's World is the unofficial name for the semi-nightmarish parallel world of wilderness where most of the story of Don't Starve takes place. All of the main characters in the game seemed to have originated from the "Real World" and are transported to the world through Maxwell's Door.
Maxwell's World, somewhat contrary to the name, seems to be mostly controlled by Them. However, after Them imprisoned Maxwell on the Nightmare Throne, he gained the power to control the world in many ways, such as being able to create many of the world's creatures through an unknown method of experimentation.
The World appears to be quite similar to the Real World in various ways. It has a Day-Night cycle, Seasons, Biomes, as well as many creatures which tend to be similar to their "Real World" equivalents such as Crows, Gobblers, and Beefalo which are similar to the "Real World" Crows, Turkeys, and Cattle. On the contrary though, there are also many creatures that are different from their Real World counterparts. For example, Pigs have become semi-intelligent bipedal humanoids, capable of basic speech, and seem to be the dominant species on the Surface World as shown by their villages and farms. Rabbits, although a lot like real-life rabbits, have short little horns as well as their ordinary ears, which cause them to appear more like the fictional "jackalopes" from the Real World's folklore. Spiders come in many different types, are all larger than real Spiders, and live in communal nests.
Even though there are many similar animals, Maxwell's World is home to many unique and, in most cases, frightening creatures. There are flightless and violent Tallbirds, Summer and Winter Koalefants, and the Winter giant, Deerclops. In the Reign of Giants DLC, the Moose/Goose, Dragonfly, and Bearger are other seasonal giants encountered in Maxwell's World.
While the maps in Don't Starve mostly take place on islands, it is possible that there is more to the world than just the islands. When Maxwell examines the Moose/Goose, he says that he doesn't know what it is, only that it's from the North. This makes it possible that there are many other areas in Maxwell's World that are currently unknown to even Maxwell himself, but not necessarily to Them.
Littered around the islands are Sinkholes whose Caves lead to the Ruins of a long extinct yet once proud Ancient Civilization of what seemed to have been arthropodal creatures who eventually destroyed themselves and most of their culture through the overuse of Nightmare Fuel. It is possible that they were once the dominant species on the planet until Them, and eventually Maxwell, gained control of the world. The second possible explanation is that Them are the Ancient Civilization itself, or at least it's afterlife, shapeless form, that they might have become with their magic experiments.