It means the folder is visible in the folder list - it's required if you share a subfolder (otherwise how will they see the subfolder if the folder its in is not visible?)
Read permissions controls whether they can see anything inside the folder and write controls if they can add items to the folder. It's required on all folders in the path (including the mailbox root) if you share a subfolder - but contentls of the folders will be hidden if that is the only permission given.
For example, if i have visible permission to your folder but none for read and nothing set for write, i can see it but i get an error if i try to open it. I can't save things to it. If you want to share a calendar subfolder with me permissions will look like this:
Mailbox root (Outlook Today) - Visible permission. None for read, nothing for Write.
- Calendar - Visible permission. None for read, nothing for Write
-- Shared subfolder - visible permission, read permission.
When i expand the folders, i only see the folder names, not the contents.