Hypnosis:

1. Hypnotic trance; an altered state of awareness ('trance') in which unconscious or dissociated responses to suggestion are enhanced in quality and increased in degree ('hyper-suggestibility').
2. Hypnotic induction ('hypnogenesis'); the process by which hypnotic trance is induced in the operator ('auto-' or 'self-hypnosis') or in others ('hetero-hypnosis').
3. Hypnotism; the field of study which encompasses, among other things, hypnotic trance; its induction, management, and application; and related subjects such as the phenomena of 'waking suggestion' and naturally occurring ('hypnoidal') trance states. (Abbrv. of 'neuro-hypnotism' meaning 'sleep of the nervous system.')

Hypnotherapy: The use of therapeutic techniques or principles in conjunction with hypnosis.

First of all, the name hypnosis can often be misleading.  It comes from the Greek word “hypno” meaning sleep, but in hypnosis the subject never actually goes to sleep, it is only the nervous system that sleeps.  German-born physician Anton Mesmer (that’s where we get the word mesmerise!) is often—and incorrectly—credited with having discovered hypnosis.  In fact, his beliefs were more spiritual and supernatural than psychological, leading him to his theory on “animal magnetism”.  It was James Braid, a Scottish doctor, who first discovered hypnotism in 1841, and coined the phrase “neuro-hypnotism” or nervous sleep.  Having followed Mesmer’s work on “animal magnetism” he developed the theory of hypnotism as “a peculiar state of the nervous system, induced by a fixed and abstracted attention of the mental and visual eye, on one object, not of an exciting nature.” [Braid, Neurypnology, 1843]

It wasn’t until some 40yrs later that French philosopher Hippolyte Bernheim wrote “I define hypnotism as the induction of a peculiar psychical condition which increases the susceptibility to suggestion.” So in the nutshell, hypnosis is a state of sleep of the nervous system that facilitates the subconscious acceptance of suggestion.