It means no longer hosting your own server for sending email, but rather use eg smtp.gmail.com to send outgoing mail. It would mean allowing Gmail.com to send email from your domain via SPF, thus allowing all with a Gmail account to spoof your from domain/header.

Ed: as sibling correctly notes, "smart hosting" specifically referes to setting your smtp server to relay via another (eg: Gmail) - eg exim or postfix allow setting a "smart host" so that rather than looking up the receiving smtp server, all mail is shunted to the smarthost to figure out.

Added: you might get good delivery to Gmail using Gmail smarthost (requiring you to have a Gmail account) - but you might need to use outlook.com as a smarthost to get good delivery to o365 accounts... Etc.