In what follows we shall discuss the uniqueness of the days between Yom Kippur and Succoth.
"On the first day, you must take for yourself a fruit of the citron tree..." (Leviticus 23:35). The "first day" mentioned here is actually the fifteenth of the month of Tishrei. Why, then, is it referred to as the "first day"? The Midrash explains that it is the first day of the year regarding the calculation of man's sins. That is, after the pardoning of sin on the tenth of Tishrei, Yom Kippur, a new calculation does not begin immediately. Rather, it is delayed until a few days later, on the first day of Succoth.
"On the first day, you must take for yourself a fruit of the citron tree..." This, says the Midrash, is in fact the fifteenth, and so why does the Torah call it the first?! Rabbi Manna and Rabbi Yehoshua brought the following analogy in the name of Rabbi Levi: This can be compared to a town that owed the King a large sum of money in taxes, and he went to collect them. When the King came within ten kilometers of the town, the leaders of the community went out to praise him. He was glad, and therefore cancelled a third of their debt. When he came within five kilometers of the town the ordinary citizens went out to praise him. The King responded by canceling another third of their debt. When the King entered the town itself, all of the people - men, women, and children - came out to praise him, and so he cancelled the entire remaining debt. The King said, "I'll let bygones be bygones. I have renounced all past debts. Now we will start the calculation anew."
Similarly, prior to Rosh HaShannah, the leading rabbis of the generation fast and humble themselves before God, and the Almighty pardons them for a third of their sins; from Rosh HaShannah until Yom Kippur, additional individuals fast and humble themselves before God, and God pardons another third of their sins; on Yom Kippur everybody fasts, men women and children, and the Almighty says to the Jewish people, "I'll let bygones be bygones. Now we will start the calculation anew." And from Yom Kippur until Succoth all of Israel is busy with Mitzvoth, one with his "Succah," another with his "Lulav." On the first day of Succoth the entire Jewish people stand before the Almighty with their "Lulavim" and "Ethrogim." The Almighty says, "I'll let bygones be bygones. Now we will start the calculation anew." Therefore, Moses warns the Jewish people, "On the first day, you must take for yourself a fruit of the citron tree..." The first day in the calculation of man's sins. These are the words of the Midrash.
Rabbi Avraham Yitzchak HaCohen Kook provides an underlying reasoning for the above Midrash, answering the question why is it that the during the days between Yom Kippur and Succoth man's sins go unrecorded. Rabbi Kook says that on Yom Kippur the act of repentance elevates a person to a very high level, and the light of the World to Come shines upon him. Because of this elevation one becomes distanced from the present world, and when one finally returns to the affairs of this world he needs to guard himself from any sort of stumbling block. The days between Yom Kippur and Succoth are directed towards preparing man for his return to the affairs of this world in a suitable and sacred manner. The transition involved in descending from the height attained on Yom Kippur to normal daily existence is not so simple. It is possible to lose proportion. During the four days after Yom Kippur the proper balance has not yet been attained and the sanctity of Yom Kippur covers up for everything.
From here we see that just as in order to reach the high level of Yom Kippur there is a need for a gradual process extending from the first of the month of Elul until Yom Kippur, so too, the decline from this high level to the normal daily existence of this world must come about in stages. One must neither be allowed to fall suddenly nor to remain elevated. In the first days, then, while the proper balance has not yet been attained, there is no reckoning of wrongdoing. Only from the first day of Succoth, when fulfilling the Mitzvoth of Succoth and Lulav, do the affairs of this world become grounded and properly attached to sanctity, and for this reason it is the first day of reckoning a person's sins.