A house or home is certainly an intuitive enough concept for digital use, but its origin is a little more involved than that.
The web is built on the general model of a file system, in keeping with its origin as, essentially, a standardized protocol for accessing files on other people’s computers. It’s why we have such incomprehensible URLs, with slashes and no spaces — that’s how paths to files were originally encoded.
In a shared file system, users have access to some files but not others. Alice’s files would be in C:\Users\Alice, while Bob’s would be in C:\Users\Bob (the slash direction depends on many things). These personal file locations were officially called “home directories,” directory being the technical term for a folder or similar organizational unit.
When these files became accessible first to others on the system, then eventually via the web, the home directory became the main page where content was stored. So you would go from Bob’s home directory /Bob into subdirectories and pages like /Bob/projects or /Bob/about.html (as you still do in URLs — this is the basis of HTTP) and when you were done, go back to the home directory or homepage. Of course when one thinks of a home, a house (of Western style, notably) is the most commonly associated image. So home directory became homepage became home, now meaning whatever origin page you choose in your web browser.