The Rokeiach writes that just as it was the norm to circle a city before attacking, as we find Bnei Yisroel did before their battle against the city of Yericho, likewise, on Sukkos we circle around the Torah (with the four species). Rav Wolbe (Da'as Shlomo) explains the Rokeiach's perplexing comparison as follows.
When Bnei Yisroel prepared to attack Yericho, it wasn't merely the physical wall surrounding the city that hindered their entrance. There was also a spiritual wall inside their hearts that had to be abolished through the blowing of the shofar and the encircling of the city. Just as back then Bnei Yisroel had to destroy this "internal wall", so too, each year on Sukkos we must destroy the internal wall inside of us that hinders our connection with Hashem.
What is this "internal wall?" Didn't we achieve forgiveness for our sins on Yom Kippur, thereby ridding ourselves of all deterrents to our avodas Hashem? The answer is that we did achieve forgiveness, but we still live in the same world, and it is this world that blurs our view and prevents a proper connection with Hashem. Feelings of permanence in this world, an attraction to the culture and allure of the other nations, and an erroneous outlook that nature is something separate from the Creator, all come together to comprise this spiritual wall.
It is amazing to take note of how on the Yom Tov of Sukkos, we attempt to "destroy" the many aspects that comprise this division. Firstly, the Torah tells us, "Leave your permanent abode and go into a temporary abode." The Torah isn't negating the need to live properly; rather, it is merely setting our priorities straight: the next world is the true world and this transient world is preparatory.
Additionally, the Medrash (Parshas Emor) says that the four species symbolize the four letters of Hashem's Name. In other words, when one sees nature he should be able to distinguish Hashem behind this facade. According to the Ramban (Drashos) it is for this reason that we read Koheles on Sukkos. We are trying to ingrain in ourselves that there is no nature; everything is controlled by Hashem, and it is to Him that we will have to ultimately answer.
The Haftoros read on the first day of Sukkos and on Shabbos Chol Hamoed describe the days of Moshiach when all the nations of the world will recognize Hashem's omnipotence. Reading and thinking about these prophecies help us quash the lure toward the culture and lifestyle of the other nations.
Sukkos culminates in the Yom Tov of Shmeni Atzeres. After succeeding in breaking down the spiritual wall that divides us from Hashem, we merit the connection toward which we have strived. On Shmeini Atzeres we don't eat in the Sukkah, shake a lulav or eat matzah. We simply spend the day with our Creator. May we be zoche to achieve this awesome connection!
Chag Kasher V'Sameiach!