What is a 'private' timecard and which timecards can be set to private?

Timesheets Admins can make current and future timecards private, so only authorized people can see them. See Configure Advanced Settings: Company Timesheets.

Private timecards are only visible to the creator of the timecard, the user the time is being tracked for, and administrators of the Timesheets tool. Additionally, if the privacy is enabled, the following will apply:

• Only admins of the project level and company level timesheets can see all timecards in the project tool

• The company admin permission level will take precedence over any project-level permissions.
  For example, if Jane is an admin to the company level timesheets tool and has standard permissions at the project level, then Jane would still be able to see all timecards in that project since she can see them at the company level.

• Users with 'Standard' level permissions can only see the timecards they created.

• Users with 'Read Only' level permissions can only see timecards for their own hours.

• CSV exports and Reports are impacted at the project and the company level.

Which timecards can be set to private?

The privacy setting only affects the visibility of timecards in the Timesheets tools. It does not change the privacy of timecards in the company level Timecard tool and the Daily Log Timecard module.