The significance of the Succah booth, on the simplest level, is to remind us that God protected and preserved the Jewish people in the desert by housing them in such dwellings after taking them out of Egypt. By dwelling in the Succah we reenact this experience.
A broader historical perspective offers us a deeper insight into the meaning of this observance. Passover celebrates the Exodus, which was the physical creation of the Jewish people. Shavuot celebrates the giving of the Torah, our spiritual creation. Succot celebrates the remarkable physical survival and continuity of the Jewish people, the result of the ongoing and all-encompassing Divine providence.