Of all the mitzvot, rituals and customs of Rosh Hashanah, blowing the shofar stands out as the most potent of all its symbols. The physical action of blowing the shofar entails breathing deeply in and then blowing out. This action is reminiscent of the description of the formation of man in Genesis: "and God blew into his nostrils the soul of life" (Genesis 2:7).
It is explained in Kabbalah and Hasidic thought that God blowing into man the soul of life mirrors in an allegorical manner the way a person first gathers air into his lungs from the diaphragm, the deepest recesses of his inside, in order to afterwards blow out fully. It is thus understood that the soul of man emanates, as it were, from the deepest essence of God. This idea is an essential foundation of Hasidism and is expressed in the teaching that the soul of man is "a portion of God Above" (paraphrased from Job 31:2, as taught in the second chapter of Tanya). When Rosh Hashanah is called in the prayers the "birthday of the world," it means the creation of the physical universe in general, but more specifically, the anniversary of the creation of man. In this light we can understand the blowing of the shofar on Rosh Hashanah as the remembrance of God blowing into man the soul of life.
While the physical action of blowing the shofar is from inside-out, the action most associated with Yom Kippur is just the opposite -- from the outside-in. Throughout the night and day of the Yom Kippur fast we continually take our clenched fist and tap our hearts, hoping to arouse repentance and remorse for our actions. The prayers of Rosh Hashanah begin the 10 day period of repentance in a general fashion, while the prayers of Yom Kippur hone in on the details. The thoughts, speech and actions of the previous year, all of which began within us and moved outside us to affect the world around us, are all brought back inside, to be reviewed, rectified and atoned for.
The holiday of Sukkot, following the contemplative days of Rosh Hashanah and Yom Kippur, is in essence a continuation of the same repentive process, but with a special emphasis on joy and integration. What begins on Rosh Hashanah as ethereal and idealistic longings and promises of the heart must now be actualized and brought into practical reality. Shaking the four species (palm, citron, myrtle and willow) represents the integration of the inside-out action of Rosh Hashanah with the outside-in action of Yom Kippur. This is accomplished by shaking the four species to the six directions of space, by first holding them close to the heart and then shaking outwards, followed by bringing them back to the heart. All the most inner, deep-felt prayers of the previous holidays born in the heart and mind must now find practical ways to manifest themselves in the outside world. The in-out, out-in, motion of shaking the four species is a potent symbol of unification and actualizing our goals and hopes for the new year.
The integration which takes place during Sukkot is further represented by circling the synagogue once each day of Sukkot and then seven times on the seventh and last day of Sukkot called Hoshanah Rabbah. The holiday cycle, now drawing to a culmination, is symbolized by these seven circuits of the synagogue. Some Hasidim have the beautiful custom of blowing the shofar after each circuit, in order to emphasize the entire process beginning on Rosh Hashanah is now coming to a close. Just as the Jews marched around Jericho seven times and then blew the shofar, causing the walls to come down, this is our chance to break down any last psychological walls still standing between us and God.
An element of Yom Kippur is added to Hoshanah Rabbah by those who have the custom to wear their special holiday robe, a kittel, as they did on Yom Kippur. Though we usually think of Neila, the last prayer of Yom Kippur, as representing the "closing of the gates" of the 10 day period of repentance and atonement, we are taught that the final seal is actually on Hoshanah Rabbah. This is symbolized by hitting five willow branches on the ground five times, reminiscent of the hitting of the heart on Yom Kippur. Additionally, many of the prayers and the way they are chanted during the 10 days of repentance are repeated on this day. Hoshanah Rabbah thus takes many of the elements of Rosh Hashanah, Yom Kippur and Sukkot and weaves them inside-out and outside-in.
Whereas during Sukkot we shake the four species and make one circle of the synagogue daily, on Simchat Torah we "shake" ourselves by dancing joyously with the Torah scrolls. The dancing of this day is the true integration of all the previous holidays and their various inner and outer actions and symbols. The constant circling brings us to a place where inside-out and outside-in weave together in perfect harmony and unity. As we finish the Torah on this day, we immediately roll it back to the very beginning and start again, the epitome of the statement in the Sefer Yetzira: "Their end is enwedged in their beginning and their beginning in the end."