A private account is when a user has turned their account to "Private" from their settings screen.
When your account is in Private:
1) Only users YOU ALLOW can follow you.
2) All your streams will automatically toggle to private.
3) Your archived videos will only be visible to users YOU ALLOW to follow your account.
Private Stream - A private stream is one that ONLY THE PEOPLE YOU FOLLOW can view.
Private Video - A video that ONLY THE OWNER can see.