Chabad - What is a rebbe?

The following translated excerpt from the writings of the Lubavitcher Rebbe is from Chabad.org

There are also nesi'im who are channels in several of these areas, or even in all of them.

Such was the nature of the leadership of the nesi'im of Chabad, from the Alter Rebbe to, and including, my father-in-law, who embraced all these categories and areas: they nurtured their chassidim in both the "internal" and the "encompassing" qualities of their souls; in Torah, divine service and good deeds; in spirit and in body. Thus, their bond with those connected with them was in all 613 limbs and organs of their souls and bodies.

Each and every one of us must know--that is, dwell upon and implant the awareness in his or her mind--that the Rebbe is our nassi and head: that he is the source and channel for all our material and spiritual needs, and that it is through our bond with him (and he has already instructed us in his letters how and by what means this is achieved) that we are bound and united with our source, and the source of our source, up to our ultimate source on high.

The following also from Chabad.org explains why the above concept is not a violation of having intermediaries

Israel, too, is comprised of many "organs" and "limbs." There are the great sages of each generation who devote their life to the assimilation of the Divine essence of Torah, whose entire being is permeated with the awareness of G-d's truth. These are the mind of the nation. Israel has a heart, individuals whose lives exemplify compassion and piety; and hands, its great builders and achievers. Each and every individual, from the "Moses of the generation"5 to the ordinary "foot soldier," forms an integral part of the body of G-d's firstborn -- each is equally "the limb of the father."

But as with the physical father-child relationship, it is the mind of the child which facilitates the bond with his father. As long as the many organs and limbs of his body remain a single integrated whole, they are all equally the father's child. The mind is not serving as an "intermediary," G-d forbid -- every part of the body, including the toenail, possesses the self-knowledge that makes the two ostensibly distinct bodies of the father and child a single entity. But it is only by virtue of their connection to their mind that this awareness resides within all the child's parts.

The same applies to the "body" that is Israel. It is our life-bond with our "mind" -- the sages and leaders of Israel -- that both integrates us as a single whole and imbues us with our connection to our Creator and Source.