Private Team Folder
Team Folder in the past was managed by administrators. Administrator can create, edit, delete team folders. The team folder can be published to a group of users, including Active Directory group. It is very convenient to share files and folders with a group of users in the same team.
As team groups bigger, it may not be convenient for administrator to manage all the team folders. So it makes sense for administrator to assign some users to be able to manage team folder that they own themselves.
It usually starts with the role manager by creating a role with Add/Edit/Delete permissions and assign it to users or Active Directory groups.
Manage Team Folder
The user who are in the private team folder role will be able to manage team folders without seeing all the team folders from everyone.
Here is a YouTube Video about private team folder