http://technet.microsoft.com/en-us/library/bb124423.aspx
An accepted domain is any SMTP namespace for which a Microsoft Exchange organization sends or receives e-mail. Accepted domains include those domains for which the Exchange organization is authoritative. An Exchange organization is authoritative when it handles mail delivery for recipients in the accepted domain. Accepted domains also include domains for which the Exchange organization receives mail and then relays it to an e-mail server that’s outside the Active Directory forest for delivery to the recipient.
Authoritative Domains
An organization may have more than one SMTP domain. The set of e-mail domains for an organization are the authoritative domains.
Relay Domains
When e-mail is received from the Internet by an Edge Transport server and the recipient of the message isn’t part of an authoritative domain, the sending server tries to relay through the Exchange server. When a server acts as a relay server that has no restrictions, it can put a large burden on Internet-connected servers. Administrators can prevent this open relay scenario by rejecting all e-mail that isn’t addressed to a recipient in the organization’s authoritative domains. However, there are scenarios where an organization wants to let partners or subsidiaries relay e-mail through the Exchange servers. In Exchange 2010, you can configure accepted domains as relay domains. Your organization receives the e-mail messages and then relays the messages to another e-mail server.