The day after Moses’ descent from Mount Sinai on Yom Kippur, his father-in-law Jethro encountered him attempting to singlehandedly judge the Jewish nation. This prompted him to offer advice:
You will surely wear yourself out…for the matter is too heavy for you; you cannot do it alone. Now listen to me [and] I will advise you…You shall select from the entire nation men of valor…and you shall appoint over [Israel] leaders over thousands, leaders over hundreds, leaders over fifties, and leaders over tens. They shall judge the nation at all times, and it shall be that any major matter they shall bring to you, and every minor matter they shall judge themselves. This will make it easier for you, and they shall bear [the burden] with you (Exodus 18:18–22. Rashi to ibid. 18:13).
The day after Moses’ descent from Mount Sinai on Yom Kippur, he gathered the nation of Israel and instructed them to construct a Mishkan so that G‑d’s presence would dwell among them. The Jews eagerly brought all of the necessary materials, exceeding what was needed for the task (Exodus ch. 35. Rashi to ibid. 35:1).
Tachnun (confession of sins) and similar prayers are omitted.
It is customary to begin working on -- or at least planning -- the construction of the sukkah immediately after Yom Kippur. Indeed, The Midrash (Vayikra Rabbah 30:7) describes the four days between Yom Kippur and Sukkot as a time when the Jewish people are "preoccupied with mitzvot... this one is occupied with his sukkah, this one is occupied with his lulav..."
According to an old Chassidic tradition -- mentioned in the writings of the Baal Shem Tov -- the day after Yom Kippur is referred to as "G-d's Name." (The Baal Shem Tov explains that each of the various divine names describe G-d's involvement in a specific "world" or realm of reality, but the designation "G-d's Name" -- without reference to any particular name -- connotes a divine effluence that transcends all realms and particulars. On Yom Kippur, we access and reveal the very essence of our soul, which is one with the very essence of G-d; thus the day after Yom Kippur carries the designation "G-d's Name.")
On Yom Kippur, the souls return to connect to their origin, carrying with them the divine sparks from all they've done in this world.
Their return rises like an aroma of burning incense through the atmosphere, and through endless strata of spiritual realms, until it reaches a place beyond higher and lower. It reaches the essence of G-d.
And there it becomes the essence of pure and ultimate bliss.
On Sukkot, that divine, supernal delight reappears in our world, much as a cloud condenses from the vapor rising from the sea.
And it manifests as the branches and leaves covering our Sukkah.
So that within the Sukkah, we are embraced by G-d’s delight in us, and we rejoice.