A "domain" is the glue that joins a page set and theme to a domain name. (A domain name is, eg, www.example.com, examples.com, test.example.com.)
As a domain name need to be created and configured externally (registered and DNS provided) a domain is generally created by a super-user admin. A company will have predefined domains, to create another ask a higher grade administrator.
A use of multiple domains could be:
- mobile and normal themes for one set of pages
- development and release sites.
The "domains" button shows a table of the available domains, the left column is used to select, the remaining links in the table are just convenience links.