Domain aliases allow more than one domain name to access the same website.
Domain alias will simply allow your primary website domain to be accessible using the domain alias. The visitor will get a HTTP status 200 OK and the website will be displayed as normal.
(Note that the HTTP status is processed by the visitor's browser and not actually seen by the visitor on their screen. In both cases everything happens automatically without user interevention and very quickly.)
Common uses for domain aliases would be if you have multiple corporate names or variations of the corporate name.
For example, you may have a primary website domain name "alphabetagamma.com". You can setup a domain alias "abg.com" so that anyone who also navigate to this URL will see the same website.
Using domain aliases can have a negative impact on your site raking in many search engines and thus you run the risk of losing a lot of traffic from visitors to your site who follow a search engine link. To avoid this you can use 301 redirect. Read more about 301 redirect: http://billing.wsigenesis.com/knowledgebase/18/What-is-a-301-redirect.html
Note: You must acquire domain registry for the primary domain as well as the domain names you will use for domain aliases.