Why Does The Torah Remain Closed?
All reserve disappears in the exuberant dancing of Simchas Torah.
Every Jew feels a natural desire to take a Torah scroll in his arms and celebrate.
Hidden resources of joy, energies which we did not know we possessed, surface at this time.
The source for this happiness, the center of attention, is of course the Torah. Yet, throughout the entire Hakkafos celebrations, the Torah is never opened; we dance holding it wrapped in its mantle.
Furthermore, on Simchas Torah people do not usually add to their usual schedule of Torah study; if anything, the opposite is true.
Though the Torah is usually associated with disciplined study, on Simchas Torah we approach it differently, singing and dancing in a manner that bears no apparent relationship to understanding. 
The Core of the Torah
The reason for these innovations on Simchas Torah is that intellect is not the only means through which a person can connect with the Torah.
One dimension of the Torah can be defined and grasped by our minds; another dimension is infinite, beyond all human comprehension.
The infinite aspect of the Torah represents its essence, for "G-d and His Torah are one." 
Just as G-d is infinite, transcending all bounds and limitations, so too is the Torah, extending beyond the confines of human understanding.
Accordingly, for man to relate to Torah, his commitment must mirror this infinity.
Thus, when our ancestors received the Torah at Mt. Sinai they declared,  Naaseh venishma ("We will do and we will listen"), thereby making a superrational commitment to follow G-d's will, a commitment that was not conditional upon their understanding.
By first stating Naaseh ("We will do"), they demonstrated that they were willing to follow G-d's commands without reservation.
The intellectual dimension of the Torah is crucial, but does not define its essence.
So that man could relate to G-dliness, the Torah was brought down from its infinite heights and invested in rational concepts, laws and principles that can be studied, understood and incorporated into our behavior.
These, however, represent merely the external dimensions of Torah and not its inner core. 
Garbing the Torah in intellectual categories is a process of outreach by G-d to man.
On Simchas Torah, however, man reaches out to G-d and attempts to connect with the aspect of Torah that is one with Him.
This requires stepping beyond the restrictions of one's own rational mindset.
And this is precisely what takes place when a Jew dances with a Torah scroll on Simchas Torah. 
Dancing Together as One
All Jews, learned and unsophisticated alike, share equally in the Simchas Torah celebrations, because these celebrations tap a point in the soul which, by nature of its infinity, defies the entire concept of rank and gradation. At this level of soul, no difference exists between one Jew and another.
The basic commonalty that links us all makes us join hands and dance together, oblivious to the personal differences that might otherwise create barriers between individuals. 
The "Feet" of the Torah
The Rebbe [*] used to say  that on Simchas Torah, the Torah itself wants to dance; however, since a Torah scroll has no feet, we Jews must function as its feet and carry it around the dais in the synagogue. 
A foot has no independent will; it is totally subservient to the head that controls it, obeying its wishes without question.
So deep and complete is our surrender to the Torah on Simchas Torah, that we are lifted beyond the realm of our individual identities and become the "feet of the Torah."
This metaphor reminds one of the need to advance in Torah throughout the entire year, for the feet are associated with marching forward.
This progress affects the Torah as well as the Jewish people, for just as the feet can bring the head to a place it cannot reach alone, the Jewish people can elevate the Torah and bring its essence to the surface.
In light of this, we can appreciate the place of Simchas Torah in the sequence of holidays beginning with Rosh HaShanah and Yom Kippur.
All of these holidays focus our attention on the inner core of our relationship with G-d.
Simchas Torah, as their climax, is the point of transition between the intense spiritual experience of the month of Tishrei and our daily, down-to-earth circumstances.
This safe landing is navigated by means of the rejoicing of Simchas Torah.
At that time, our joyous awareness of how "Israel, the Torah, and the Holy One, blessed be He, are one,"  lays the groundwork for our divine service throughout the entire year.
These celebrations enhance the bond with G-d and the Torah that is unconfined by the limits of intellect, in every aspect of our conduct throughout the year.
Moreover, these celebrations anticipate the ultimate celebrations that will accompany the coming of Mashiach and the advent of the Era of the Redemption. May this take place in the immediate future.
Adapted from Likkutei Sichos, Vol. IV, Simchas Torah
* Rebbe Rayatz - Rabbi Joseph Issac Schneerson
1. See Sefer HaMaamarim 5686, p. 55.
2. Zohar I, 24a; II, p. 60a; see also Tanya, chs. 4 and 23.
3. Shmos 24:7; Shabbos 88a.
4. From this perspective, there is no difference between a verse a child learns from the Chumash and a Talmudic dissertation delivered by a sage. Both are media in which G-d has invested Himself to allow man to relate to Him. The core of both experiences is not the simplicity or sophistication of the medium, but the inner bond with G-d that is established.
5. Afterwards, however, the Torah must be studied closely so that this essential bond is integrated into one's thought processes. Indeed, the Hakkafos circle the dais on which the Torah is read and they are introduced by a responsive reading of the verses beginning Atah hareisa. These practices are a reminder that even the boundless celebrations of Simchas Torah remain connected with the Torah's intellectual content; the rational and superrational dimensions of the Torah cannot be separated from each other.
6. See the above essay entitled "The Unity of our People," which speaks of the unique element of Jewish unity that characterizes Simchas Torah.
7. Sefer HaSichos 5704, p. 36.
8. Thus we can understand the description of the holiday as "the season of our rejoicing": not only is this happiness shared by the entire Jewish people, but the Torah itself also shares in this joy.
9. Cf. Zohar III, 73a.