Gmail has a feature that lets you send mail from a different email address. For non-Gmail addresses, you could send email addresses using Gmail's SMTP servers or through the email provider's SMTP servers. Now you can
no longer use Gmail's SMTP servers for new accounts:
We rolled out a change for new accounts where if you would like to send mail as from a non-Gmail or non-Google Apps account, you can no longer use the option of Gmail's servers to send your mail. Google is a strong supporter of email authentication standards including DKIM, SPF and DMARC. This is one in a series of changes to strengthen email authentication, and end any practices by Google products which break authentication.
Any accounts which previously were using Send Mail As via Gmail servers will not be affected, you can keep the previous set up. If you are a Google Apps user sending from a domain alias or email alias you can also check out the steps listed in this help center article under "I'm a Google Apps for Business user sending from a domain alias or email alias".
The help center article has more information: "Your other email provider has to provide authenticated SMTP support for you to use this option. We'll use TLS by default, or SSL if you enable it. Many email services that provide POP or IMAP support also offer authenticated SMTP support, and you can likely find your SMTP server configuration instructions alongside information about POP or IMAP."
Until 2009, all the addresses you added to your Gmail account used Gmail's SMTP servers. In 2009, Gmail added the option to
use the email provider's SMTP servers. One of the benefits was that email clients like Outlook no longer displayed "From username@gmail.com On Behalf Of customaddress@mydomain.com". At that time, Google mentioned that "we recognize that your other address might not have a server that you can use to send outbound messages — for example, if you use a forwarding alias rather than an actual mailbox, or if your other email provider doesn't support authenticated SMTP, or restricts access to specific IP ranges. For this reason, we've kept the original method as well." Now, the original method is no longer available.
{ Thanks, Jan Willem Hengeveld. }