I think that any horsemanship, including anything that is labeled as "natural", varies among individuals/trainers, so I'll just describe what I do that means natural horsemanship to me:
1. Any training is to be started and progressed only according to the psychological and physical needs, possibilities, maturity and health of the individual horse. Young horses are let to mature as long as possible before any physically harder work.
2. Any training is to be based on the body language and psychology of the horse, first making sure that all the horses' needs are met, e.g. - feeding, socializing, movements, etc. are as close to the natural needs of the horse as possible.
3. The goal of the training is to let the horse discover himself as a proud and powerful being, making all the circumstances such that they motivate him to give me his full potential, and to co-operate with me as a trusted leader.
4. All the reactions are to come from communication, not restriction, and with as little technical aids, as possible.
5. The tack is to be as little invasive as possible, and just to support the horse, not to alter him into what he wouldn't be able to do without the tack. It must not harm the horse in any way - physical or emotional.
And, of course - "Be as soft as possible, but as firm as necessary."