There are a handful of private forums that I know of which got the search-engine indexing disabled. They are based on condominiums, software companies, and only allows its members and prevent 3rd party access
We have a couple of private forums on here, staff forums really and one for premium members with laxed rules
We usually only have a few private forums on my forum and they are for staff members and also a recycle bin which gets any deleted posts moved into it. We did once have a VIP forum which was private however it didn't do too well so we gave up on it and just kept open forums for members.
Their purpose is to organize a group of people discussing something that's not meant for a wider audience. Maybe warez, some software development, stuff like that. Content for a small group of people and nobody else.
You also have private forums for premium members on some big forums. It's something only them can see.