The word Neuro refers to an understanding of the brain and its functioning. Linguistic relates to the communication aspects (both verbal and non-verbal) of our information processing.
Programming s the behavioural and thinking patterns we all go through. There is a relationship between perceptions, thinking and behaviour that is neuro-linguistic in nature.
NLP was developed in the early 1970's by Richard Bandler, Ph.D., an information scientist, and John Grinder, Ph.D., a linguist. Bandler and Grinder were interested in how people influence one another, and in the possibility of being able to duplicate the behaviour.
Their early research was conducted at the University of California at Santa Cruz. What made their search special was their use of technology from linguistics and information science, combined with insights from behavioural psychology and general systems theory, to unlock the secrets of highly effective communication.
Much of early NLP was based on the work of Virginia Satir, a family therapist; Fritz Perls, founder of Gestalt therapy; Gregory Bateson, anthropologist; and Milton Erickson, hypnotist. It was Erickson's work that formed the foundation for a lot of NLP, thus the tight connection with hypnosis.
People like Milton H Erickson and Virginia Satir seemed to have a magical effect on people who came to them for help - 'healing' them with just a few words compared to years of repetitive 'traditional' therapy.
Satir asked questions which changed the way people thought. She challenged people's internal rules and brought them to the surface where they could be dealt with.
NLP has several techniques for diagnosing and intervening in certain situations. There is a technique for phobia's, a way to diagrammatise past traumas, ways to identify and integrate conflicting belief systems that keep you from doing things you want, etc.