A duet is the same session on the second reformer, with someone you choose. Your sister, your friend, your partner, your daughter. You still get hands-on cueing, and you still get corrected.
It works best when the two of you are at roughly similar points, because the session moves as a pair. If one of you is brand new and the other has trained for years, a private each will serve you both better.
Plenty of people start in a duet because it is less daunting than being alone in a room with an instructor. That is a perfectly good reason.