G-d instructed Moses to tell the Jewish people,"You must live in huts (sukkot) throughout this seven-day period."
The sukah is unique among the Torah's commandments in that it is the only one that we physically enter; the sukah surrounds us on all sides. This property of the sukah is a physical manifestation of the Divine energy that the sukah embodies: the awareness that G-d exists apart from the world and beyond its limitations.
We are taught that spiritually, the sukah derives from the cloud produced when the high priest would burn incense in the Holy of Holies on Yom Kippur. Whereas the animal sacrifices focused primarily on refining our human/animal soul, our Divine soul operates on a higher plane than that of our normal, human/animal consciousness. The Divine soul enables us to transcend the limits imposed on our lives by our human/animal soul, whose intellect and emotions are focused solely on physical things.
Thus, our task on the holiday of Sukot is firstly to focus on G-d's unlimited Divinity by building the sukah, and secondly, to internalize our awareness of this Divinity both by dwelling in the sukah and by fulfilling the commandment of holding and waving the four plant-parts.