The private round feature allows you to record your round without anyone knowing you are on the course. Scoring is just like on a normal round; the only difference is that nobody can see that you are on the course. You can even play with your friends, but the live leaderboard doesn't show your name except to you and your playing group.
The private mode can be activated from the advanced settings in the game setup.
Toggle the private round switch, and you're good to go.
Note: The private round feature is available only with a Gold membership.