The Group feature in Moodle is pretty handy if you have multiple blocks of a course and/or have two (or more) teachers sharing a course.
1. How to Turn Group Function on:
Turn editing on > Edit Courses Settings > Groups > Group Mode = Visible (or separate)
2. How to make groups:
Course Admin > Users > Groups > Create Group
3, How to make an assignment separate per groups:
Turn editing on > Toggle the icon beside your assignment to be "Visible Groups"