This privacy feature allows hiding the mobile number of a contact from other users on your account. The users will still be able to schedule calls for this contact but they won't be able to see or edit the contact's mobile number.
The mobile number can be "locked" when creating or editing a contact via the Contacts page or while scheduling a call.
If another user on your account schedules a call for this contact the contact's mobile number will be hidden on all pages viewed by this user. Below is an example of the 'Schedule a phone call' screen using contact with a private mobile number as the call recipient.
The 'contact owner' (the person who made the mobile number private) will be able to see the mobile number on all pages.