People are said to be in rapport when they are in a privileged situation for communicating. When in this situation people just seem to be able to get their messages through to one another. On the other hand, if two people are in rapport and a third is not then this will be quite apparent, for everyone. This is a pretty common situation which can often be observed in restaurants for example with two people in a deep conversation and a third looking disconnected (not in sync when laughing for example).
NLP puts much emphasise on the concept of rapport as it is better to be in rapport to execute a number of the other techniques (such as using the Milton Model for example).
Achieving of rapport
NLP suggests a number of techniques for achieving rapport. Pacing (synchronisation) is one. Pacing is the action of matching yourself to your interlocutor. Matching can occur on many levels. One can for example match posture and movement. You can also match verbal qualities (speed of speech, voice tone and pitch, ...). Literature often mention going as far as matching breathing patterns. You can also match values and beliefs... The basic idea which is pushed to the extreme here is that most people like people who are like them. Of course, one must be careful while pacing not to appear to be monkeying (which definitely isn't any good for rapport).
An interesting NLP concept is that matching brings rapport and vice versa, that is rapport brings to matching. The action of using rapport to bring someone to match you is called leading, hence the pace/lead terms.
Once rapport is achieved it can be used in many ways. One is to simply gain trust, for example to obtain information in therapy, or to convince the patient to follow the healing process. Another way to use rapport is to lead someone to match whatever you want (for example in the sales process). You can also use rapport to shift someone's internal state, physiology or internal representations (for example to influence behaviour). This last example uses the reciprocity of rapport and synchronisation.