Tzadik is an ordinary Hebrew word for a righteous person, used throughout the Bible and the rabbinic literature without any technical weight. What happened in the eighteenth century is that the Hasidic movement gave it one. In Hasidic teaching the tzadik is not merely a person who behaves well but a conduit: the blessing that descends on a community is understood to pass through him, and attachment to him is a means of approach that is available to people who cannot reach it through study. Arthur Green's analysis reads the developed doctrine as making the tzadik an axis, a point at which the upper and lower worlds meet, and traces the imagery back through earlier kabbalistic material.
The institutional consequence was the court. A tzadik gathered followers who travelled to him, ate at his table, sought his blessing and asked his advice on matters far outside religion, and the position descended to his sons, so that Hasidic dynasties formed and are still identified by the towns their founders lived in. The movement is therefore not one thing: Chabad, Breslov, Satmar, Ger and many others descend from different courts and differ from each other considerably.
This was also the central charge in the opposition to Hasidism. The Mitnagdim, the opponents, led from Vilna in the late eighteenth century, regarded the elevation of a living man to that position as a displacement of Torah study and a step towards something worse. The dispute was bitter, involved bans and denunciations, and although both sides long ago made a working peace against shared external pressures, the theological objection has never been withdrawn.