The Repository includes all of the usual document library functionality with the exception of the Edit Offline action and the ability to create Google Docs content.
Just as in a document library, the explorer panel includes navigation and filtering options. This lets you filter the repository contents by category or tag, or you can browse the repository file structure. You can also choose to view the content items currently checked out to you (I'm Editing view) or those that you've specifically flagged as favorites (My Favorites view).
The functionality available within the Repository library is identical to what you find in a site library. See Working with content in a library for details on performing specific actions within the Repository.