Fields will show {Private} or blank while viewing a Profile Display page if the user has their field set to private within their Profile Form. Below is a breakdown of different visibility, depending on what type of user is viewing the page:

Supervisor
May see {Private} when viewing the Profile Display of its own account.
Will see true field values when viewing another constituent's Profile Display page. For example, if the user has email address set to Private, the Supervisor will see the true email address and will not see Private or a blank field.

User
If the user is logged in and viewing their personal profile display page, they will see {Private} next to the true value of the field. For example, the user has their email address marked private in their profile form. When viewing the profile display page, they will see "{Private} myemail@email.com. 

Public
If a public user, not logged in, is viewing a Profile Display page, which is also public, fields that other users marked private will be blank. 


Additional Resources
How to make directory or profile fields public or private by default
How can a user update their Directory field privacy?
How can a user change the privacy of fields on their Profile Form Display?
Fields appear blank in Directory or {Private} in Profile Display