Updated Requirements for SMTP Relay through Exchange Online

mkcj1984 

>Can you explain exactly what "Relay" means? I think there is some confusion on the very nature of what kind of relaying is meant by this?

Answer:  Relay is an SMTP (Simple Mail Transfer Protocol) term. This is from RFC5321:

A relay SMTP server is usually the target of a DNS MX record that
   designates it, rather than the final delivery system.  The relay
   server may accept or reject the task of relaying the mail in the same
   way it accepts or rejects mail for a local user.  If it accepts the
   task, it then becomes an SMTP client, establishes a transmission
   channel to the next SMTP server specified in the DNS (according to
   the rules in Section 5), and sends it the mail.

"Relay" in the blog means O365 receive email from your org and send the email for you to the final destination. For example, your org has domain contoso.com you want to send email from your environment (or hosted mailbox in O365) to an internet domain, such as outlook.com, yahoo.com, gmail.com or fabrikam.com;  using the sender domain contoso.com.  For this path, we require you after the change, to configure Inbound OnPremises connector (Your Environment -> Office 365 in connector UI) which is an existing requirement, in addition use sender domain consoto.com as the SMTP envelop sender address (MailFrom), or use contoso.com as the certificate domain (SAN or alternative domain) to send the email to O365 for "Relaying" purpose.