Rapport is the sense of "being in touch" with another person. It creates a sense of connectedness. It is equally important in NLP and in hypnosis, which refers to two totally different concepts in each. Thus there are two kinds of rapport to understand.
NLP-style rapport:
Enter the other person's model of the world, to seem to be like the other person, to gain their confidence and trust in order to build rapport. As people like people who are like themselves, they tend to be attracted to those who are most like themselves. When you are in rapport with another person, you've entered their model of the world.
Eg. Pace the other person's physiology by mirroring their body language and matching their language patterns without being obvious. Use the same speech predicates as the person you are building rapport with, by noting the representational system that they are consciously using: Visual, Auditory, Kinaesthetic. Remember always using the other person's system! Speak in this system, and offer back the other person's own exact descriptive words or the very words as closely as possible instead of interpreting, to send the same picture they have in their head back to them with their own identical words. This gives them the impression that you are in complete empathy with them. Speaking in the wrong system would be more counterproductive, while using visual and auditory words if you know the other person are accessing kinaesthetically.
Hypnotic rapport:
Unconscious rapport between a hypnotist and subject, whereby the subject only tend to pay attention to (or respond to) only the hypnotist, and will typically pay no attention to anyone else.
Tip: Use the exact same words as someone else to intensify rapport, does not mean to copy the person, but reflect back, on occasion, the exact words of someone else.
Eg. Say "I once heard..." to the other person.
Rapport is not only a general skill which is well worth practising in therapeutic situations, but also a fundamental tool for life itself. By applying rapport skills, you will rapidly build a connection with anyone. You will become far more influential, building conversational bridges into long-term relationships.
