What is a domain name? Usually it is the identifier associated with your organization's email address (like @ example.com). The domain you provide will be used for all your Google services. For example, if you choose example.com or mail.example.com, you will be able to create user accounts for john@example.com or jane@mail.example.com.
Don't have a domain name? You can sign up for Standard Edition, purchase a domain name, and then upgrade to Premier Edition.