The Talmud tells us an interesting hypothetical conversation that takes place between Hashem and the non-Jews. They would claim that if they were given a second chance to accept the Torah they would keep it just like the Jews do. Hashem says to them, “I have little Mitzvah called Succah. Go keep it.” Immediately they will go and build a Succah and enter it. Then the sun starts beating down and in the heat they will all exit the Succah and trample it down. This is a test given to the non-Jew.
In truth Jews are also tested. After going through a period of Asseret Yeme Teshuvah and after fasting and praying during an entire day of Yom Kippur, when we reach the highest level of spiritual feelings, we are told immediately to go out and build a Succah.
This is a test for us. It is not sufficient to reach a high state of spirituality but we must leave the security of our home and go out into the world. There, with all its trials and tribulations, with all its enticements and temptations, we have to prove our faith and live up to the dictates of the Torah. If we succeed we have passed the test.
That is why Succot follows on the heel of Yom Kippur. We must demonstrate that our faith is not only theoretical but is actually our very existence.