A Board Only folder can be created when there are documents that are to be restricted for the Board Members eyes alone.
Only people with a tick in their Board Member box can see or access a Board Only folder. See Managing People to set a person as a Board Member.

Board Only folders can be managed by:
Board Secretaries
Chairs or Administrators who are also Board Members (have a tick beside their name)
To make a folder Board Only:
Make a title
Tick the box. (This is only shown to those with administration access).

3. Add Folder
When the folder is created there will be a lock beside the title showing that it is restricted.
On the right hand side, under the context menu, there is the option to un-restrict this folder.

Things to note with a Board Only Folder:
The folder is not able to be viewed by anyone who is not set as a board member box.
A file/document that is inside a Board Only Folder cannot be uploaded into an agenda
Sub-folders of restricted folders are also restricted.
Useful links:
Roles and Permissions
Add a Folder
FAQ's on Folders