At the bottom of the assignment page are three buttons: The Cancel button will cancel your work. The Submit button will send your assignment to your instructor for grading. The Save As Draft button will save your assignment but not send it to your instructor.
If you click Save As Draft then your instructor will see that you are working on your assignment. It will be "locked" on your instructor's page, but your instructor will not be able to view your saved files until you hit the Submit button and submit your assignment.
Be sure to hit the Submit button when you have completed your work in order to actually send it to your instructor.