I believe it is a way of training a horse by putting pressure on him until you get the desired response then removing the pressure. Pressure comes in all forms, from just a look to a smack on the butt or worse. It's a way of communicating with a horse in a way he understands. He feels pressure, looks for the right answer and when he finds the right answer the pressure goes away. Some horses take more pressure to achieve the correct response than others.
This is what horses experience in the wild when dealing with relationships within the herd. Thus the name of natural horsemanship. It is not about using pain, fear or intimidation to train a horse. It's not about being all lovey-dovey with your horse and it's not about being rough or mean with your horse either.
I can tell you that I practice "natural horsemanship" and have had great results with it. That is not to say that if my horse bit me he wouldn't be REALLY sorry! Because he would! But the thing is...he wouldn't bite me because he sees me as his leader and he respects me. He is not frightened of me, he respects me. I guess that's what it's really all about, respect. And I respect him too. He's a 1,000 lb animal that could easily kill me so I do respect him and treat him with love, kindness, fairness and firmness when necessary.
I would like to hear what other people think "Natural Horsemanship" is. How would you describe it?