I find the following explanation from Rabbi Shalom Dov Ber Schneerson to be a understandable explanation of TzimTzum:
http://www.chabad.org/library/article_cdo/aid/83687/jewish/Chapter-XXVII.htmThe great underlying principal of the torah, as R' Akiva taught is to "love your fellowman as yourself". And indeed, Torah literature in general and Chassidus in particular overflows with instructive and inspiring advice on how one may bring oneself to truly love one's fellow. Reading this literature, to be sure, is far more cheering than dwelling on disharmony and baseless hatred. But the reality of the human condition cannot be ignored and the present discourse addresses itself to that all too human problem.
Borrowing the mystical terminology of Kabbalah and Chassidism, this book deals with the spiritual roots of baseless hatred, its cosmic repercussions, and its attainable remedies.
This in-depth discussion of the spiritual seeds of divisiveness and dissension did not sprout in a vacuum, nor was it meant to be studied in a vacuum. It was meant to be used. In response to its call, anyone who calls himself a Chassid will surely concede that whatever his spiritual stature, there is still room for making his own interpersonal contacts less judgmental and less abrasive, a little mellower and a little humbler.
On Ahavas Yisrael
Chapter XXVIIIn order to better understand this matter we must first explain concealment and revelation in [the context of] their original source.
Our Sages declared:1 “In the beginning of the world’s creation there was first darkness and then light.” There, too, was darkness and light, concealment and revelation, and there too was their unification light and revelation out of darkness and concealment, and concealment out of revelation.
The teaching of the Etz Chayim2 [on this matter] is well known. Before the first tzimtzum [contraction and concealment of the infinite light], also referred to as the “vacant space” (Makom Panui), the Ein Sof -light filled all space. Nothing existed other than the revelation of the [infinite] Ein Sof -light. Concerning this it is stated,3 “Before the world was created there was only Him and His Name,” and likewise,4 “You are holy and Your Name is holy.” So, too,5 “You are One and Your Name is One.” The “Name” refers to the level of Malchus [“Kingship”] of Ein Sof , also called shmo hagadol and shmei rabbah (“the great Name”), which is truly included in G-d’s absolute Essence.
Afterwards He contracted Himself, retracting the first light totally, and submerging it within the essential Being of the Ein Sof. All that remained was a trace6 of the original light, one solitary point like the point of a yud. This point included within itself all that could possibly be revealed in the order of hishtalshelus [the progressively descending levels of existence. And only] this point remains after the tzimtzum because the worlds cannot receive the original light. G-d therefore contracted and concealed the light within Himself, and there remained only the point, the merest glimmer which could be revealed.
The aforementioned7 analogy of a mashpia (a person who transmits) and a mekabel (recipient) is pertinent here. Because the essential light of the mashpia cannot be assimilated by the mekabel , he has to conceal the depth of his wisdom within himself. There then remains only a simple point, that which can be revealed to [and assimilated by] the mekabel. Similarly, when the essential Supernal light was concealed, there remained only the residual point,8 that which could relate to the worlds.
However, [because] this point is still in a state of concealment, there [still must be] drawn from it the kav (“line”) or chut (“thread”), a revelation of light. The first stage of its enclothement was in Adam Kadmon,9 which was the first existence created through the kav. This level is called an “area” [of expression of light] and is referred to as Tehiru Ila’ah (“the Supernal purity”) which follows the tzimtzum. Of this it is said,10 “He carved an engraving in Tehiru Ila’ah.” The entire hishtalshelus from the first to the last level even to the very lowest level is all included in Adam Kadmon. This matter is discussed elsewhere.
We find therefore that there are two types of “light.” The first is the original light which preceded the tzimtzum , when the Ein Sof -light filled all of space; and the second is the light of the kav after the tzimtzum. The first light was the original revelation which shone forth from the Ein Sof. This is [the light which was] then contracted and concealed, leaving only a point which was still concealed. [And finally,] out of the concealment of the point came the revelation of the light of the kav.
This being so, we have here a paradox. On the one hand, the first revelation of the Ein Sof -light gives rise to the concealment which constitutes the first tzimtzum ; indeed, [even] the point that remains is also concealed and utterly lacking in expansion. On the other hand, the concealment of the point gives rise to the light of the kav or chut.
We can accordingly interpret [the text of the prayer],11 “He rolls away light before darkness and darkness before light,” as follows: G-d rolls away the original Ein Sof -light that preceded the tzimtzum , before the darkness and concealment of the tzimtzum , and conceals [His light] within the “point.” He then rolls away the darkness, i.e., the tzimtzum , before the light of the kav which shines forth after the tzimtzum.
Summary:
The [original] source for revelation and concealment and their unification. [The stages in the process of the revelation of G-d’s light]: the light before the tzimtzum , the tzimtzum and the trace [which exists] as a point, the light of the kav.