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, email@example.com. 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 firstname.lastname@example.org and set it to point to email@example.com.
You can only set up an alias on the same domain; you would be unable to cross domains. For example, you could not have firstname.lastname@example.org be an alias of email@example.com. In order to accomplish a forward like that, you would need to log into the firstname.lastname@example.org mailbox, and set up a forward in the mailbox settings to email@example.com