The sefarim tell us that each of the shalosh regalim of Sukkos, Pesach and Shavuos correspond to the three forefathers (avos). Pesach corresponds to Avraham Avinu, Shavuos to Yitzchak Avinu, and Sukkos to Yaakov Avinu. The scriptural source for this is the passuk in Vayishlach, which tells us that after Yaakov's encounter with Esav, he went to a place called, 'Sukkos' and he made sukkos for his animals. This teaches us that there is some kind of connection between Yaakov and the festival of Sukkos . What is the link between the two?
In order to answer this, it is instructive to examine an interesting feature of Sukkos. On Sukkos, even the most mundane activities, such as eating and sleeping, become Mitzvos. The mere act of sitting the in the Sukkah turns these activities that are normally devarim shel reshus into mitzvos, that obligate one to say the bracha of 'leysheiv basukkah'. Therefore, a person who spends most of his time in the sukkah, is constantly performing the mitzvo of living in the sukkah. In this way, Sukkos has a tremendous power in that it elevates a person's daily activities into acts of great kedusha (holiness).
This aspect of Sukkos can help understand some differences between Sukkos and the other chagim. The Kol Bo notes that one says the bracha for being in the Sukkah throughout the whole chag. In contrast, on Pesach, the Kol Bo holds there is also a mitzvo to eat Matzo for the whole 7 days, and yet we only say a bracha on the first day - why do we not say every day? He answers that when a person eats matzo on the later days of Pesach, it is not apparent that he is doing so because it is a Mitzvo. He could be eating the matzo simply because he is hungry and has no option to eat bread. In contrast, on Sukkos, there is no practical reason to eat in the sukkah, one could equally easily eat in his home. The fact that he davke eats in the sukkah indicates that he is doing so purely for the sake of the mitzvo. He can say a bracha throughout the whole of Sukkos, because he demonstrates that he is only performing the normally mundane acts in of sleeping and eating because it is a mitzvo to do so in the sukkah.
The Ben Ish Chai applies the concept that merely living in the sukkah is a mitzvo to answer a different question about Sukkos. Unlike Pesach and Shavuos, Sukkos is described as zman simchaseinu,(the time of our joy). The other chagim also represent times of great happiness, so why is Sukkos considered more joyful than them? He answers that the extra joy of Sukkos is because of the mitzvo to sit in the sukkah that applies throughout the whole festival. This constant ability to perform mitzvos for the honor of the festival arouses a great sense of joy. He writes that this on the other festivals there is no essential difference between a person's daily life from the rest of the year. Accordingly, one may not have the constant awareness of the festival that he has on Sukkos, resulting in a lower level of joy. This is the reason that Sukkos in particular is mesugal for simcha. Thus, we see that Sukkos is unique in that it elevates normally non-holy activities into mitzvos, and enables us to have a constant awareness and joy of the festival.
How is this aspect of Sukkos connected to Yaakov Avinu? Of all the avos, Yaakov Avinu was the one who was most required to be deeply involved in the daily vicissitudes of life such as dealing with dishonest people, spending long hours at work, and bringing up a large family. For many years he was forced to deal with areas of reshus, unable to devote all his time to learning and prayer. One aspect of Yaakov's greatness is that he was able to live in such an environment and elevate his daily activities into acts of holiness. This is what he declares to his brother, Esav, when he returns from his long years in exile. "I lived (garti) with Lavan". Chazal tell us that the word, garti, spells, taryag, which represents the 613 mitzvos. Yaakov was alluding to the fact that he had remained steadfast in his avodas Hashem, despite living in adverse conditions.
It seems that many aspects of Yaakov Avinu relate to the fact that he was able to elevate the mudane into kedusha. Chazal tell us that the avos desribed the Beis Hamikdosh, (and avodas Hashem by extension), in different ways. Avraham described the Beis Hamikdosh as a har (mountain), Yitzchak as a sadeh (field), and Yaakov as a bayis (house). These various descriptions represent the different ways that the avos related to avodas Hashem. Why does Yaakov describe it as a house? A house is the location of all the mundane activities that a person performs throughout his daily life, including eating, sleeping, and forms of work. Yaakov elevated all such activities because he saw them all as opportunities for holiness. Accordingly, he viewed a house as a vehicle of avodas Hashem.
In a similar vein, the avos represent the three daily prayers. Avraham corresponds to shacharis, Yitzchak to mincha, and Yaakov to maariv. Maariv is different from the other prayer services in that it is described as a reshus, a non-obligatory prayer. Why is Yaakov, in particular associated with an optional prayer? In light of the aforementioned explanation of Yaakov's ability to turn non-obligatory activities into mitzvos, we can also understand why maariv corresponds to Yaakov It represents the fact that a person wants to connect to Hashem even though he is not obligated to do so.
Yaakov also corresponds to the third bracha in the shemoneh esrei, that of kedusha. This also fits in with the above explanation. The Torah definition of kedusha is not merely avoiding the physical world, rather it is sanctifying it so that it too can be used a tool of avodas Hashem.
With this understanding of Yaakov and Sukkos, their connection is obvious. Both represent taking optional activities and making them holy. It is easier to feel pious when involved in obviously spiritual activities such as learning and praying. However, it is far more difficult to connect to Hashem whilst eating, sleeping and working. Sukkos is the only time of the year when such actions become mitzvos merely by doing them in the sukkah. Of course, this does not mean that we can indulge in gluttony and over-sleeping whilst being in the sukkah. Rather it obligates us to focus on the fact that our mere dwelling in the sukkah is a great opportunity to help us develop our awareness of Hashem and to be more lishma in our going about our daily lives. If we do this, then we can take the recognition that mundane acts are great opportunities for kedusha, into our daily lives even when the festival has left us.