Facebook Messenger and WhatsApp are huge. That's probably not exactly news though. WhatsApp notably has more than one billion active users while Facebook Messenger has crossed the 900 million active user plateau (though there's likely quite a lot of overlap in those user bases). Now, Facebook has announced how many messages the services process, and the number is rightly huge.
At the annual F8 developers conference yesterday, Mark Zuckerberg said that activity on Facebook Messenger and WhatsApp combined is now at 60 billion messages a day. For comparison, all of the SMS messages sent globally is just 20 billion per day. Although, it's unclear how accurate that SMS statistic is, because that's the same figure that made the rounds in January 2015 when WhatsApp announced it was processing 30 billion messages
per day. While it's possible that SMS usage hasn't grown since then, it seems unlikely.
However, that also leads to a question about the Messenger plus WhatsApp stat. WhatsApp has added more than 300 million active users since announcing that it processed 30 billion messages per day by itself and Facebook Messenger has added more than 200 million users since last year's F8 conference (again, there's probably overlap in those numbers). So, either Messenger doesn't add much to the message total, or the activity levels of those "active users" is flattening out.