The last day of Sukkot has its own rituals
Reprinted with permission from The Jewish Religion: A Companion, published by Oxford University Press.
Hoshanah Rabbah, or the "Great Hoshanah," is the seventh day of the Festival of Tabernacles [Sukkot]. According to the Mishnah (Sukkah 4: 5), in Temple times, on the Festival of Tabernacles, huge willow branches were placed around the altar and a circuit was made around the altar while the worshippers recited: "Hoshanah" ("O Lord, deliver us") (Psalms 118: 25).
On the basis of this Temple practice, it became the custom on Sukkot for the worshippers to hold the four species (the palm branch, the etrog [citron], the willows, and the myrtles), and make a circuit around the bimah [pulpit] while reciting Hoshanah hymns in which God is entreated to deliver His people, especially from famine and drought, since Sukkot is the festival on which the divine judgment for rain is made.
Practices on Hoshanah Rabbah
On the seventh day of the festival, there are seven circuits, at each of which a special Hoshanah hymn is recited; hence the name, Hoshanah Rabbah.
After the seven circuits, the four species are put aside and bunches of willows are taken in the hand and these are beaten on the ground three times so that the leaves fall off. The usual explanation of this rite is that it is a symbolic representation either of the rain, required at this season, which beats on the leaves, or of the leaves which fall from the trees until these are revived by the rain.
Further elaborations were introduced under the influence of the Kabbalah in which this day is seen as the culmination of the penitential season beginning on Rosh HaShanah and continuing through to Yom Kippur. Part of the service is chanted in the solemn mode of Rosh Ha‑Shanah and Yom Kippur, the Reader wears white robes, and references are made to the 'sealing' of human destiny for the year ahead.