An alias is an email address that forwards all the mail it receives to another email address (or several) that you specify.
For example, you could create an alias called firstname.lastname@example.org for which all the mail would be automatically forwarded to you at another account, email@example.com. If you wanted, the email sent to "firstname.lastname@example.org" could be forwarded to more than one address, for example, email@example.com and firstname.lastname@example.org.
Alternatively, you can set up multiple aliases and have them forward to the same email. For example, you might have email@example.com, firstname.lastname@example.org, email@example.com all forward email to firstname.lastname@example.org.