One of the central Chassidic practices (darkei haChassidus) is that Chassidim are to travel regularly to the Rebbe for a one-on-one meeting, which is known in Chassidic parlance as Yechidus. This meeting has classically been the cornerstone of the Rebbe-chossid relationship.
In the preface to Tanya, the Alter Rebbe beautifully describes his special relationship with the chassidim who came to seek his advice in Yechidus: “Words of affection were common between us, and they revealed before me all the hidden aspects of their heart in matters of serving Hashem related to the heart.” See also the Alter Rebbe’s words in Mei’ah She’arim p. 58 (cited in Likkutei Sichos, Vol. 5, p. 334): “ ... One cries out in Yechidus at one’s distance from the living G–d.”
First, these sources show that although advice is sought in this meeting, it is much more than a patient visiting a doctor and receiving a prescription. It is a unity between souls in an awesomely deep, personal, and loving relationship, in which profound mutual love is expressed.
The explanation of this deep relationship is that a Rebbe is a Neshamah Kelalis, a “general soul,” of which the chossid is an individual component. When the perat, the individual aspect, connects to its soul-origin directly, this is a very profound, personal experience.
There are so many beautiful stories in Chassidic lore of the deep relationship between chossid and Rebbe, and how chassidim would yearn to go to Yechidus, and prepare for it for a long time, and regard it as the highest point in their lives.
We also see from these quotes that Yechidus is a place for the chossid to express his deepest yearnings, viz., to perform Torah and Mitzvos with true love of Hashem and fear of Hashem, to reach true Teshuvah, and thus a truly intimate connection with G–dliness.
(For a Hebrew booklet on the concept of Yechidus, see here.)