NLP is a base of knowledge and understanding of how the brain works to promote different behaviours, changes in physiology and thought processes - together with tools (in the form of mental exercises and specific procedures) to literally CHANGE YOUR MIND. When people do something different they often say "Oh I changed my mind" - and that's exactly what they have done! NLP provides a means to instant, positive change when you are stuck in behaviours, situations or states of health that are unwanted.
Neuro refers to the nervous system and its connections between brain, body, emotions, movement, behaviour.... and all aspects of us being human.
Linguistic refers to the affect language has on us - the words said by other to us, words we say "in our head" (as our brain provides a running commentary) and words we use in everyday speech to describe ourselves, situations and our "world"
Programming refers to the mental programmes and patterns we operate, out of our awareness, as we live day to day.
Put all three together and you have NLP - the way in which language and the nervous system work together to influence our mental patterns and programmes. It was originally developed to enable people to excel at what they could do with average competence. However, the techniques and processes have evolved over time to help people change unhelpful/unwanted memories, behaviours and reactions so that they feel more in control and much more comfortable with who they are, as well as how they respond and behave.