Announcements and Messaging are useful Moodle tools instructors can use to communicate with their students. Announcements should be used to communicate with the entire class. Messages are used to communicate with a single student.
To send a private message to a single student:
Clicking the icon will open the message.
The student can reply, using the Write a message… box.
For more information, see: https://docs.moodle.org/35/en/Messaging