The seventh day of Sukkot is called Hoshana Rabbah, and is considered the final day of the divine “judgment” in which the fate of the new year is determined. It is the day when the verdict that was issued on Rosh Hashanah and Yom Kippur is finalized.
The Midrash tells us that G‑d told Abraham: “If atonement is not granted to your children on Rosh Hashanah, I will grant it on Yom Kippur; if they do not attain atonement on Yom Kippur, it will be given on Hoshana Rabbah.”
Isaiah says,1 “They seek Me day [after] day.” The Talmud explains2 that these two “days” refer to the day when the shofar is sounded (Rosh Hashanah) and the day when we take the willow (Hoshana Rabbah)—the day when the heavenly judgment begins, and the day when it concludes.
In addition, on Sukkot we are judged regarding how much rain will fall in the upcoming year.3 Thus, on Hoshana Rabbah, the final day of Sukkot, this judgment is finalized. Considering how much our wellbeing and economy depend on bountiful rainfall, it is clear how important this day is.
To read about the deeper significance of this mitzvah, see One Twig and One Leaf.