From Discworld & Terry Pratchett Wiki
The Hermit Elephant (Elephantus Solitarius) is a species native to Howondaland. The Hermit Elephant has thin skin making another form of protection necessary; it enters a village and lifts a building onto its back to use as a shell. As the elephant grows larger it will require bigger and bigger houses. The Hermit Elephant is similar in this way to the Roundworld hermit crab.
The Science of Discworld III suggests that the God of Evolution was evicted from Dunmanifestin for inventing this creature. A small herd of these animals are kept at the Palace menagerie; they contributed (copiously) to Geoffrey's collection in The World of Poo.