Let say you have a domain and you want to have also an email service. With the new Gmail for your domain, you can use the Gmail technology to manage emails. Even more the mails are hosted and managed on Google’s servers.
For the moment, the service is available as a limited beta and you want to sign up, you will need (of course) a Google Account and to answer to some questions about your email needs.
The sign-up is available here. Google launched GMail as a new service in 2004 and ever since the company added constantly new features.