Forward seat is just the correct position for riding in a hunt seat saddle. Alternately, you could ride in a western/stock seat position, or in a classical seat position as in a dressage saddle. Forward seat position is relatively new to the world of English riding, introduced by Frederico Caprilli around the turn of the last century. The Wikipedia article offers a description of the pre-Caprilli jumping seat and the differences between the two. Federico Caprilli - Wikipedia, the free encyclopedia
Forward seat includes comparatively short stirrups, a more compressed knee, the seat in contact (usually fairly light contact, as compared to Classical/dressage seat or western) with the saddle on the flat, and a straight and relaxed back - perhaps inclined very slightly
forward. The concept behind adopting this seat is to maximize the horse's freedom of movement without compromising rider security, especially in the context of jumping. The two point position is part of the forward seat concept, practically adopted when the horse jumps. In two point, the rider's hip joint closes and the seat comes out of contact with the saddle as the rider matches the horse's movement through the air.
Riding in the forward seat (i.e., shortened stirrups, more angle to knee, slightly forward inclination, etc.) in a western saddle isn't a bad thing necessarily, depending on the context. Many contesters and game riders I know ride with a position much more akin to a jumper than a WP rider - forward seat better facilitates the horse's freedom of movement around a barrel as well. I also see endurance riders or more hardcore trail riders with a more forward seat position, again to maximize freedom of movement, or to allow the horse to more safely and comfortably take a jump or other obstacle on the trail - from the forward seat, it is a simple matter for the rider to come into 2-point as the horse's movement requires. A lot of people that switch back and forth between tack have a slightly forward seat in western, or a slightly back-on-the-pockets position in English. I'm a major example of that, especially the former.
However, if you're planning on entering the world of WP or Stock Seat equitation classes, you'll need to adopt a more standard western seat. A Stock Seat Eq judge will rightly dock points if your position is more like that of a jumper. Most western disciplines entail the western saddle and positions for practical reasons as well, as the jumpers do with their own gear and position.
Hope that was helpful to you! As bsms said, a couple of lessons if you're confused can do wonders - it can be tricky to really understand and apply things like position changes just from reading the mechanics. Sometimes you just need someone on the ground to help you fine-tune things. The Jumping subforum I'm sure also has some great info on 2-point position, getting it, and finding/fixing faults in it.