When your company registers with Microsoft Online Services, it is assigned an Internet domain name similar to yourcompany1.microsoftonline.com. This domain is intended to be used while evaluating Microsoft Online Services. If your company has registered an Internet domain name, you can add that domain to Microsoft Online Services. This will allow usernames such as  john@contoso.com as opposed the default john@contoso1com.microsoftonline.com

This 3:23 video by Arvind Suthar demonstrates how to add a domain via the Microsoft Online Services Administration Center, and verify your domain managed by the Domain registrar NetworkSolutions.com

General Domain information can be found here. Domain verification procedures specific to some of the most popular domain registrars can be found here