This teaching expresses the greatness of the Baal Shem Tov, the Maggid of Mezeritch, and the Alter Rebbe, and explains that through learning their Chassidus, we connect with their lofty level.
The Tzemach Tzedek writes about the Alter Rebbe: Also from my grandfather, may his soul rest in Gan Eden, we heard predictions of the future [that were fulfilled] to a hairsbreadth [i.e., with total precision].
This appears difficult to understand: Does the Tzemach Tzedek mean to praise the Alter Rebbe for miracles, which are a superficial thing? Does this define the Alter Rebbe’s greatness? Rather, this comes in continuation to what is written there earlier: He [the Baal Shem Tov] and his student, the Maggid [of Mezeritch], would see from one end of the world to the other with a seeing eye ...
This was possible because the light that was created on the first day that G–d hid in the Torah was revealed before them. Of this the Tzemach Tzedek says “also from my grandfather, may his soul rest in Gan Eden, we heard predictions of the future ... ” The expression “also” implies that the “predictions of the future” expressed by the Alter Rebbe is the same idea as what was written earlier concerning the Baal Shem Tov and the Maggid—the revelation of “the light that was created on the first day.” However, the Alter Rebbe perceived this in a manner “[that was fulfilled] to a hairsbreadth.”
“The light that was created on the first day” is a reference to the light that transcends the Hishtalshelus, and “the light that reveals G–d’s very Essence.” Although this light shone for the Baal Shem Tov and the Maggid even in the physical world, the Alter Rebbe had the additional quality that this light shone in a settled manner—“to a hairsbreadth.”
In order for the light that transcends the Hishtalshelus to enter the world in a settled manner, the light is not enough; this can only be accomplished through G–d’s very Essence, which can reconcile all opposites. So will it also be in the Messianic age, when the purpose for which G–d created the world will be fulfilled—“to make a dwelling place for Him in the lower realms [i.e., this physical world].” [“For Him”] means a dwelling place for His Essence. G–d’s Essence will enable the combination of physicality and spirituality, such that “The glory of G–d will be revealed, and all flesh will see.” This means that the physical flesh will perceive G–dliness, and it will rest there in a settled manner.
This is the inner meaning of the Tzemach Tzedek’s expression “also from my grandfather, may his soul rest in Gan Eden, we heard predictions of the future.” The expression “predictions of the future” alludes to the revelations of the Messianic age.
The Alter Rebbe imbued all this into the teachings of Chassidus Chabad. By learning Chassidus we “take” the highest levels, and even the “hidden light,” and even higher, and this descends into the intellect of the Divine Soul, until it reaches the understanding of the intellect of the Animal Soul, until the glory of G–d will be revealed, and even all flesh will see, with the arrival of our righteous Moshiach, may it happen very soon.
 Derech Emunah 65a.  See Torah Ohr 44c.
 The “contraction,” in which G–d’s infinite light was hidden in order to make it possible for the worlds to be formed. This level of divine light stemmed from a level that transcended this one. See Sefer HaMa’amarim 5670, Noach.
 Yeshaya 40:5.
In my own words: The Baal Shem Tov and the Maggid of Mezeritch were able to see from one end of the world to another, and perceive everything that took place, including future events. The Alter Rebbe had the additional power to perceive these events with total accuracy. The reason they possessed this power was that they perceived a level of G–dliness that transcends all limitations, G–d’s very Essence as it were, such as will be revealed when Moshiach comes.
This enabled their perception to transcend the limitations of time and space. We are granted the ability to connect with these lofty levels through learning Chassidus in general. Chassidus Chabad enables these lofty levels to permeate the person, and even the intellect of his Animal Soul. This prepares us for and hastens the coming of Moshiach, when this sublime level will be revealed and permeate one and all.
The Rebbe has informed us that Moshiach will bring the final redemption very soon. Thus, everyone should prepare themselves to greet him through increasing in study of Torah, concentration in prayer, and performance of Mitzvos. In particular, the Rebbe has called for:
*acts of random loving-kindness to a fellow Jew; *material and spiritual charity; *study and dissemination of Chassidus; *study and dissemination of topics related to Moshiach and the redemption; *earnestly praying for the coming of Moshiach; *and promoting the observance of the Noahide Code amongst non-Jews.