An add-on domain is a fully functional domain that can be created from within your control panel. Think of it as having multiple hosting packages all sharing the same control panel. You can give them email addresses, forwarders, and more the same way you do for your main domain on the account.
The add-on domain will appear as a totally separate domain from your primary domain. There should be no evidence that your domain is an add-on domain to incoming traffic when they visit your add-on domain.