Chaza"l say that the Schach should be from "Pesoles Goren Ve'Yakev". Why do Chazal use the Lashon of "Pesoles", couldn't they have found a nicer way to describe the material we use for this holy Mitzva?
Says the Alter Sadigerer Rebbe (son in law of the Beis Ahron of Karlin), that Rosh Hashana and Yom Kippur are times of Teshuva Me'Yira - Repentance from Fear, and Chazal say that when we repent from fear our sins becomes like "mistakes" (zedonos na'asin ki'shgagos). However, Sukkos is a time of Teshuvah Me'Ahava - Repentance through love and rejoicing. This is a much higher level of Teshuva, and Chazal say that the sins become like merits!
This, says the Sadigerer, is the secret of the Schach. We davka take the "Pesoles"; the spoiled - the sins of our past; and through Teshuvah Me'Ahava on Sukkos, we uplift them into merits. Hashem's divine presence hovers over us in the Sukka davka in the form of our past sins, which we have merited to uplift through our repentance with love!