An Alias Domain is an exact copy of a real domain. It is useful when you have multiple domains that should all share the same characteristics.
For example, your company might own several domains: longcompanyname.com, shortcompanyname.com, and oldcompanyname.com, but you don't want to create separate users for each domain. You can set up longcompanyname.com as the primary domain and the other two as Alias Domains. Every user, alias, or list you set up on the primary domain will be available on the Alias Domains. Remote senders can use any domain name to reach your users, and the message will be delivered only once, into a single mailbox. It's a great way to consolidate your domains.