Dropbox is a section where you can submit your projects and assignments in an electronic format. This also provides the instructor with a way to date submissions and organize assignments.
You can use the assignment dropbox feature to electronically upload a copy of your assignment to a folder, where your instructor can retrieve it and mark it.
You can verify that your assignments have been submitted by using the "history" feature - and avoid that annoying habit of submitting your files over and over again, just to be sure they were sent (profs hate that!). If you can see your file listed in your "history" record, then your instructor can see your file too.
Once your assignment has been marked, you can click on the feedback icon below the folder name to view the feedback from your instructor. If you do not see an icon, then no feedback has been left.