Ok. Heading back to the actual QUESTION ASKED.... Natural Horsemanship is a way to communicate with the horse that the horse will OFTEN (not always) find easier to understand than some "traditional" methods.
NH often encourages horses to become braver by trusting the human to override their natural instincts to flee (such as the Big Green Ball that is often used in Parelli - when the horse trusts the human, it will accept the ball easier. In theory.)
For me, NH is just another useful tool to have and to know, but other methods can produce the same result or from some views a better result in some areas. (dressage ppl for example might not like NH, but thats just fine, as long as they dont go to the NH section of this site and start spouting)
And I know that riding horses isnt Natural etc, and overriding instincts isnt Natural, but its just a name, and some parts of it are more natural, such as learning from pressure and release on the longe rather than voice commands etc. Hope this helps, and was maybe more balanced than some of these answers :)