In your case Google would be the host/provider of your Gmail e-mail service and gmail.com is the domain name of the Gmail e-mail service.
Having your own domain name would allow you to keep you e-mail address even when switching your e-mail host. Which means you would not have to bother with re-registering you new e-mail address for every service or newsletter again.
yourname@yourdomain.com would always be yours no matter which e-mail provider you choose, IF they support a personal domain.