Your Inbox is an archive that stores all submitted and received files for up to 2 years. This allows teachers to access student submissions even after an assignment has been deleted or archived.
Inboxes can be cleared for staff and/or students for a "fresh start" by account superusers. To do so, access your Account Settings >> Account Management >> Feature Settings >> eBox File Visibility. From here you can set any date to hide student and/or staff files. Any files submitted or received prior to that date will be hidden from the users. If you do not set a date, files will be hidden after two years.