What is a DM on Facebook?

A DM on Facebook is a message that you get from somebody that you are currently following, or someone who publicly shared something with you.

When they send it via Facebook, it arrives in the form of an “unread” web notification (or message) at the top of your page’s timeline.

It won’t appear in your Messages tab in the Messenger app because there is no distinction between a Message and a DM when both go through Facebook Messenger.