If you're a teacher in Moodle, then this page will tell you about the major changes affecting you in Moodle 3.7
Messaging: Delete conversations in groups
Teachers may be given a capability to delete messages from users in group conversations.
Forums: More control
Teachers or others with permission can add a private reply in a forum and can manually lock discussions. See Using Forum
Badges: Competencies as a criterion
Badges may now be awarded based on competencies, (and competencies may be graded when grading activities)
Course custom fields
If enabled by admin, custom fields in the course settings may be added to provide extra information and improve searching.
Teachers can view hidden chapters in a book with the editing turned off .
Assignment: Rotate submitted PDFs
New icons allow you to change the orientation of submitted assignments for easier grading
Competencies: Filter by activity
When rating competencies, filter them by their linked activity or resource.
Lesson: Include media when grading essays
The Lesson activity now allows for teachers and students to include media in Essay type questions.