A home data center is a facility that is created, deployed and operated from a standard house or home.
It is similar to a data center facility in that it has servers, storage, networking and power and cooling resources, but is generally smaller in size and is intended for personal use.
Techopedia explains Home Data Center
A home data center is primarily created by IT enthusiasts and researchers that like a local data center environment within their home.
Typically, a home data center is housed within a room of the home. It can have anywhere from a couple of servers to hundreds in a rack mount or blade server configuration. A home data center is not as powerful as typical data centers, but it is capable enough to execute small-to-medium scale data center services.
Besides hobbyists, home data centers are also deployed by small businesses which use the facility to provide web hosting, applications and/or other services to their users/clients remotely.