The SMTP protocol was originally defined by RFC 821 in 1982 to allow mail servers to send messages to each other. A who receives an email that does not correspond to a local destination is transferred to another server according to the routing rules that have been configured.
With the problem of rejecting SPAM, email viruses and other fishing emails, programming a real email relay is of a complexity that has increased considerably. But for this subject, the relay will be content to transmit the mails, of the clients of its intranet only (which will have it as SMTP server) towards servers of the Internet, according to the domain of the destination.