EMDR stands for Eye Movement Desensitisation and Reprocessing. It is a treatment that was developed by Francine Shapiro in the late 1980s for processing traumatic memories. It involves making rapid bilateral eye movements at the same time as focussing on a distressing image, thought, emotion and body sensation related to the traumatic memory. This enables the unprocessed traumatic material locked in one part of the brain (the amygdala) to become stored in another part of the brain (the hippocampus) so that it becomes less vivid and distressing and can be stored like any other normal memory. It is not hypnosis. You remain fully conscious of what is happening and in control of the process. It does not necessarily require people to recount in detail the trauma they have experienced which is something that sets it apart from other trauma focussed psychotherapies.
Other forms of bilateral stimulation apart from eye movements may be used. These include tactile (tapping) and auditory (bilateral sounds in left and right ear). The evidence is strongest for eye movements but some people find it preferable to use tapping or bilateral auditory sounds. Its efficacy has been demonstrated by more than 40 randomised controlled trials and it is endorsed by the American Psychiatric Association, the World Health Organisation, the National Institute of Health Care Excellence.