There are three basic positions that a rider can use: two-point position, in which the rider's two legs are against the horse, while the seat is out of the saddle; three-point position, in which the rider's two legs and seat are in contact with the horse; and modified three-point position, in which the rider's two legs and only his crotch are in contact with the horse.
"Two-point position" is used during the hand-gallop and for riding hunter, equitation, and jumper courses, beginning in the initial circle and ending as the horse performs a downward transition at the end of the round. "Three-point position" is used at the walk, sitting trot, and canter, and on course only in extreme situations--such as when the rider needs the seat as a driving aid when a horse tries to refuse an obstacle, when there is such an acute turn during a jumper course that the rider must fully sit in order to execute it, or when the distances between a line of fences are set on such short strides that the rider needs his seat to reinforce his hands and back in collecting the animal. "Modified three-point position" is used occasionally during an equitation or jumper course, when the rider needs to drop his center of gravity and brace himself a little more at the thighs in order to execute a sharp turn or ride a distance set on short strides.
A major error is the use of three-point position as the "status quo" during any type of course over fences. In hunter classes, three-point position is unnecessary and makes the performance look stiff, rather than flowing; in equitation classes it is theoretically wrong, since the proper use of two-point has been established to free the horse's back of the rider's weight and to put the rider in a stationary position that allows the horse to maintain its balance at take-off, in the air, and on landing; and in jumper competition, three-point position slows the speed of the horse, which can be a critical fault in classes in which time counts.
The inappropriate use of three-point position indicates that the rider is using his seat to supplement an ineffective leg aid and/or the rider is lacking in knowledge of the basics of hunter seat riding.