Domain aliasing allows a user to type a web address into a web browser to pull up an already established website.  For example, you may have a website at www.mywebsite.com.  You also bought the domain name myotherwebsite.com.  When you alias myotherwebsite.com, users will type in www.myotherwebsite.com into their web browser (i.e. Internet Explorer) and the website at www.mywebsite.com will come up while www.myotherwebsite.com displays in the address bar.  

If a domain is forwarded, the web address in the address bar will change to the web address of the hosted website.  (If you type www.myotherwebsite.com into the address bar, the website at www.mywebsite.com will display and show www.mywebsite.com in the address bar.)