Rapport is one of the most used and well known parts of NLP. Most of the time it is wrongly explained as connecting well with other people. The term in fact comes from Milton Erickson. He discovered that if you hypnotize someone it is hard for other people to influence the hypnotized person. This is what it means to have rapport.
The Hermit Speaks. — The art of associating with men rests essentially on one’s skillfulness (which presupposes long exercise) in accepting a repast, in taking a repast, in the cuisine of which one has no confidence. Provided one comes to the table with the hunger of a wolf everything is easy (“the worst society gives thee experience” — as Mephistopheles says) ; but one has not always this wolf’s hunger when one needs it! Alas I how difficult are our fellow-men to digest! First principle: to stake one’s courage as in a misfortune, to seize boldly, to admire oneself at the same time, to take one’s repugnance between one’s teeth, to cram down one’s disgust. Second principle: to “improve” one’s fellow-man, by praise for example, so that he may begin to sweat out his self-complacency ; or to seize a tuft of his good or “interesting” qualities, and pull at it till one gets his whole virtue out, and can put him under the folds of it. Third principle: self-hypnotism. To fix one’s eye on the object of one’s intercourse as on a glass knob, until, ceasing to feel pleasure or pain thereat, one falls asleep unobserved, becomes rigid, and acquires a fixed pose: a household recipe used in married life and in friendship, well tested and prized as indispensable, but not yet scientifically formulated. Its proper name is — patience —
Gay Science paragraph 364
To think that one always needs to make rapport is a mistake. NLP offers different techniques like mirroring as a way to establish if rapport is needed. In many cases there is no need for rapport. In many other cases people have rapport automatically and trying to establish rapport breaks the rapport that was already there.
Trust and intimacy. – He who deliberately seeks to establish an intimacy with another person is usually in doubt as to whether he possesses his trust. He who is sure he is trusted sets little value on intimacy.
Human, All Too Human, part 1, paragraph 303