A snake's home is called a nest or a burrow depending on the particular type of snake. A nest represents the home of a snake that lives alone. A den is a home for snakes that live communally.
In addition to snakes that live in nests or burrows, other derivations of the species elect to live in whatever location provides them shelter and safety, including inside fallen trees or under rocks. These snakes do not establish a particular home for a period of time. A common misconception is that a snake lives in a pit, leading to the often used colloquial phrase "snake pit."