The pasuk says (Vayikra 23:42-43), תשבו בסוכות ...ימים שבעת אלקיכם 'ה אני ...ידעו למען , "You should dwell in succahs for seven days... so you will know... I am Hashem, your G-d." The Chidushei HaRim zt'l explains that the segulah of sitting in the succah is to help us believe in Hashem.
Chazal (Succah 2.) say that a succah higher than twenty amos is pasul. The Gemara explains that if a succah is high, one will be sitting in the shade of the succah's walls, not in the shade of the schach. What lesson can we learn from this halachah?
The Aruch l'Ner (end of Succah) explains that the walls of the succah represent matters of this world that seem to help a person with his needs (such as his parnassah, people who help him, his hishtadlus), and the schach represents Hashem's hashgachah from above. A person must sit under the shade of the schach. He must know that the source for all his needs is Hashem's hashgachah, not matters of this world.
Another law of the schach is that it must be cut off from the ground. One can't take a growing plant, which is still connected to the ground, and spread it over the roof of the succah for schach. What lesson can we learn from this halachah?
It is repeated in the name of Reb Shamshon Refael Hirsh zt'l that this represents not feeling dependent on the ground for our livelihood. For example, a farmer shouldn't think his parnassah comes from the ground. He must detach the plant from the ground when making the schach so he will know that his parnassah comes from Hashem and not from the ground. The same can be said for the people who rely on their real estate for their parnassah. And in general, this is a lesson for all people, regardless of whether they own property. We detach the schach from the earth to remind ourselves that our parnassah and needs come from Hashem alone, not from matters of this world.
Yet another halachah of the succah is that it must be situated directly under the heavens and not inside a house or under a tree (Succah 9.). Once again, this is a reminder to trust in Hashem alone. The Yerushalmi (Succah 2:3) teaches that lechatchilah, one should be able to see the stars through the schach. The Kedushas Yom Tov zt'l said that this is so people can look up at the sky through the schach and remember to place their trust in Hashem.
He said this explanation to his son, the Divrei Yoel, moments before his son's chasunah. He explained that this is also the reason a chuppah takes place under the heavens. It reminds the chosson and kallah not to place their trust in their parents or in anything else to support them other than Hashem alone.