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.

It means that "hosting" your own email really means hosting your inbox, and only your inbox. Because "the bigs" have basically monopolized sending email, you will tire of working through everyone blocking email from your 2-bit server. You will cave, and eventually use one of those "bigs" to do the sending half of "hosting your own email." Which means they will "see" and index all your email anyway, which WAS THE POINT most of us were TRYING TO PREVENT IN THE FIRST PLACE. I gave up about 8 years ago, and gave everything to Apple.

Your SMTP server uses an authenticated relay through (let's say) sendgrid that you pay for. Sendgrid delivers your mail using their reputation.