For authentication based on a HTML form with username and password, Apache is not involved and its realm is irrelevant. The application handles the authentication by itself and has its own user repository.

An application can delegate authentication to the web server, which does it on the HTTP protocol level. In that case you use the realm to distinguish different applications running on the same server from each other, each having their own user/password repository. The browser pops up an authentication form (no HTML involved) and uses the realm to tell the user to which application he's about to authenticate himself. The current RFC 7235 describes the realm as a "protection space".

I don't see this often these days, with the notable exception of web servers which in turn delegate authentication to a central service, for example for single-sign-on in intranets, where Apache uses mod_ntlm or mod_auth_kerb to let a Windows AD controller do the authentication