The first opinion in the Mishnah sets twenty cubits as the maximum height of a sukkah. This is about 10 meters, quite high. Anything over that height is invalid. Rabbi Judah does not believe that there is any height limit to a sukkah. The Talmud will extensively discuss why there should be any limit to a sukkah's height.
The second section of the mishnah adds three more restrictions. 1) A sukkah must be at least ten handbreadths high. Since there are 5 handbreadths to a cubit, this is about half of a meter. The sukkah must have three walls. And the skhakh, the roof of the sukkah, must make it so there is more shade in the sukkah then sun.
The Talmud begins by referring to a similar mishnah from Eruvin 1:1. In order to carry within an alley on Shabbat, one must put a beam on top of the entrance to the alley (see my Mishnah Yomit commentary for more info). The first opinion in this mishnah holds that if this beam is higher than twenty cubits it must be lowered.
The Talmud in Sukkah asks why the mishnah from Sukkah simply declares that a sukkah over 20 cubits high is invalid whereas the mishnah in Eruvin says that one may lower the beam. Why couldn't Mishnah Sukkah say to lower the skhakh?
The first answer the Talmud provides is that the Sukkah is a toraitic commandment. Therefore, a Sukkah over 20 cubits high is invalid. The Torah does not, according to the first opinion, count sitting in such a sukkah as fulfilling the mitzvah. Carrying in an alleyway without a cross beam on Shabbat is only "derabanan"—prohibited by rabbinical law. Therefore, the mishnah in Eruvin provided a means to remedy the problem by lowering the cross-beam.
The second explanation as to the difference between the two mishnayot is that when it comes to the sukkah, there are several rules in the mishnah. In order to lump them all together and use the same phrase for each, the mishnah simply taught "it is invalid." But when it comes to the cross-beam over the alley, since there is only one rule, that it must not be more than 20 cubits high, the mishnah could be more specific and teach the remedy of lowering the beam.
In today’s piece of Talmud we will see three different amoraim providing biblical sources for the 20 cubit height limit to the sukkah.
Rabbah emphasizes the word "know" from the verse. A person must dwell in a sukkah in such a way that he "knows" that he is in a sukkah. Since sukkah is synonymous most of the time with "skhakh" the person must notice the skhakh. If the skhakh is higher than 20 cubits one will not notice it.
Rabbi Zera emphasizes the word "shade" from the verse in Isaiah. The sukkah, i.e. the skhakh, must provide shade, not the walls. If the skhakh is higher than 20 cubits then the walls will provide the shade.
Abaye raises a difficulty on Rabbi Zera. Ashteroth Karnayim seem to be two large mountains. If a person made his sukkah in between these two mountains, then the mountains would provide the shade, not the skhakh. Nevertheless, everyone agrees that such a sukkah is valid.
Rabbi Zera responds by noting that in the case of Ashterot Karnayim the skhakh would provide shade, if the mountains were not there. But in the case of the 20 cubit sukkah, even if you took away the walls, the skhakh would not provide shade, at least not in the area in which he is sitting. Therefore, a 20 cubit sukkah is invalid whereas a sukkah built in the shade of mountains (or tall buildings for that matter) is.
Rava focuses on the seven day aspect of the sukkah. For the sukkah to be valid it must be built as an impermanent dwelling place. If one builds the sukkah too high, over twenty cubits, then the sukkah is invalid because it is considered a permanent dwelling place.
Abaye again raises a difficulty. There is no halakhah preventing one from making his sukkah out of walls of iron. Such a sukkah would clearly be valid even though it is permanent. So why should a twenty cubit sukkah be invalid?
Rava responds by saying that a twenty cubit sukkah must be permanent. One could not build a temporary structure that is so high. But up to twenty cubits one could build a temporary structure. Therefore, even if he uses "permanent" material, the sukkah is still valid.