A direct message (DM) is a messaging function in Twitter that allows a user to send a private message to a specific user. Unlike the normal tweets that can be seen by all the user's followers, a direct message can only be read by its recipient.
Techopedia explains Direct Message (DM)
Direct messages are private tweets that are sent between users and their followers. Direct messages can be deleted by those who sent them and they are removed from the receiver's inbox. This is a unique function in Twitter and is quite useful for taking back messages before the receiver can read them, unlike conventional email which is no longer under the sender's control once it has been sent.
This definition was written in the context of Twitter