Email aliases are virtual email addresses that forward email to a real email address. For example:
Tim has a domain of www.softball.com. He has an email address set up for himself, firstname.lastname@example.org. Tim also wants his sales questions to come to him as well, but wants those questions to be sent to another address. Tim can set up an alias of email@example.com and set it to point to firstname.lastname@example.org.
You can only set up an alias on the same domain; you would be unable to cross domains. For example, you could not have email@example.com be an alias of firstname.lastname@example.org. In order to accomplish a forward like that, you would need to log into the email@example.com mailbox, and set up a forward in the mailbox settings to firstname.lastname@example.org