In my mind, a correct two-point position means your legs are stretching down in even contact around your horse with your heels down. The only ‘two points’ in contact with the saddle should be your two legs, as your seat is elevated, and when in the correct balance there should be an invisible line connecting your shoulder, knee, and toe. Hands should be carried slightly off the neck and supported out in front of you.
Working in the two-point is great conditioning for a rider when it’s practiced on the flat. It helps stretch your heels down and helps strengthen your leg muscles. The two-point is essentially your jumping position; when you leave the ground and are airborne, you are almost always in a two-point contact following the horse (unless something has gone horribly wrong!).
The use of the two-point varies with riding style in between the obstacles. The typical North American style of riding is more forward and the riders are in a version of two-point at all times (see Katie Prudent), whereas the typical German style of riding uses a full seat (see Christian Ahlmann). Having said that, our sport is so global that I think it’s more rider preference and horse-specific nowadays. The horse I ride in the lightest position is Brighton; he is sensitive and likes a forward ride to encourage him across the oxers.