As long as you have a person's phone number and they also use the Messenger app, you can message them.
It seems like this is Facebook's way of getting you to use its app instead of texting-which presumably was how you were reaching your non-Facebook-friend before.
Facebook is also threatened by standalone messaging apps like WhatsApp and Snapchat. Facebook even considered buying Snapchat at one point. Those apps are taking traffic away from Facebook, traffic and users that would - in their absence - be happily using Facebook for messages. Snapchat has about 100 million users. Whatsapp has 350 million.
Other than that new feature, the app update will also have a new user interface that will allow you to swipe left and right to see recent conversations, a list of the people you message, and settings.
Facebook will start testing the new app today with a limited group of Messenger for Android app users.