The Briefcase is a new feature in Zimbra 5.0 and it allows your users to upload files to the Zimbra Mail Store and then have access to the files anywhere they can access the Zimbra Mail Client.
Users can also mount their Briefcase using Webdav. This way they can read/write to their Briefcase like a standard network folder. I have tested this on cadaver and GNOME (Ubuntu Linux). The path they need to connect to is:
(Note: can someone please elaborate on multi-domain setups? Does USERNAME need to be "USER@DOMAIN" or url encoded "USER%40DOMAIN")
This will open up several "special" folders, the one titled "Briefcase" is the one that you want.
The other special folder is "attachments" which will list all the attachments in your INBOX (subfolders too?) organized by type, sender, date, etc...
More detailed directions on setting this up can be found in WebDAV