The Rema (Orach Chaim 1:1) teaches, "The way a person sits, moves, and acts when he is alone in his home is different than how he sits, moves, and acts when he is in the presence of a great king. The way he speaks freely with his family is different from how he speaks when he is with a king." The Rema is teaching us that we should remember that we are always before Hashem, and then we will conduct ourselves with yiras Shamayim at all times. This lesson is especially applicable when we sit in the succah. At this time, we are before Hashem, and we should act accordingly.
Reishis Chachmah (Shaar HaKedushah ch.4) writes, "This was the custom of my teacher, the Remak. He wouldn't speak anything in the succah, other than divrei Torah, because the holiness of the succah is very great. Proof of this is the wood of the succah. It has kedushah, and we are forbidden to derive pleasure from it all seven days of Succos."
Mishnah Berurah (632:2) writes, "Since the kedushah of the succah is very great, it is proper to limit the amount one speaks there. He should only speak words of kedushah and Torah. Certainly, he should be cautious not to speak lashon hara, rechilus, or other forbidden words in the succah."
Bikurei Yaakov (639:2) writes, "The Shlah warned severely that one shouldn't become angry in the succah."
The Yesod Yosef (ch.77) writes, "When one sits in the succah and learns and davens there, he is literally in the upper worlds."
Sfas Emes (5643) writes, "Man was created to live in Gan Eden, which is the place of true joy, as we say (in Sheva Brachos), יצירך כשמחך עדן בגן. Adam was banished from Gan Eden, but there are times when a spark of Gan Eden shines. This is why people are happy when they are in the succah. The succah is Gan Eden..."
Yaaras Dvash (vol.1 drush 6) writes, "Hashem's cloud hovers over the succah. Although we don't see it, it is certain that whoever sits in the succah l’shem shamayim and learns Torah there and is happy with the yom tov and the mitzvos, Hashem's cloud hovers above him."
The Keren l'Dovid writes, "When one sits in the succah l’shem shamayim, he feels the holiness with hislahavus. He experiences the light of the mitzvah and knows that it is true that we were surrounded by the כבוד ענני. This sensation cannot be explained in words, but someone who experienced it knows it's true."
One of the laws of the succah is that it must be at least ten tefachim high. The Gemara (Succah 4:) explains that this is because the Shechinah never descended below ten tefachim. The Chesed L'Avraham and the Sfas Emes (כתיב ה"ד ב"תרמ) say that this hints at the holiness of the succah, that the Shechinah resides above it.
