The briefcase is a convenience feature that keeps 'shortcuts' to documents in the library that you can accumulate as you browse.  You can think of it as a shopping cart except that instead of items to buy, it holds documents to view.  Besides being a temporary holder of documents, the Briefcase also lets you act on those documents as a group.  For example, once there are some documents in a briefcase, you can download all of them as a single zip file.  Administrators can do more, of course.  For example, they can edit all documents in the briefcase at once - modifying common attributes such as category, domains with access, tags, etc.

 It's important to distinguish between the Briefcase and the FileBox.  The FileBox is an entirely separate repository of documents that is private to each user.  The Briefcase is also private to each user but rather than being a repository in and of itself, it simply holds shortcuts to library documents.