On each day of the Sukkot festival, after the recitation of hallel or after musaf - each congregation according to its custom - a Torah scroll is removed from the ark and brought to the bimah (where the Torah is read). The chazan and congregation say the first four Hoshanot responsively. They then circle the bimah holding the lulav and esrog and recite the longer Hoshana prayer for the respective day of the Festival, as they appear in the Siddur.
These prayers for redemption are referred to as Hoshanot because each stanza of the prayer is accompanied by the word hoshana - a combination form of the words hosha and na (bring us salvation, please).
On the first six days of the Festival, the bimah is circled once. On Hoshana Rabbah, the last day of the Festival, seven circles are made. This custom commemorates the service in the Bet ha-Mikdash during which the kohanim would circle the altar once daily and seven times on Hoshana Rabbah.
Hoshana Rabbah is the last day on which we fulfill the mitzvot of the Four Species and dwelling in the sukkah (although there are many in the Diaspora who dwell in the sukkah on Shemini Atzeret as well). The day is referred to as Hoshana Rabbah (literally, the great Hoshana) because more Hoshana prayers are recited on this day than on the other days.
This day was also known as "the day of the beating of the aravah." The Mishnah (Sukkah 4:2) records: How was the mitzvah of aravah fulfilled? There was a place below Jerusalem called Motza. They would go down there and pick branches of willows and would then come and place them alongside the altar with the heads (of the willow branches) bent over the altar. They then sounded the shofar: a tekiah, a teruah, and a tekiah. Each day they would circle the altar once and say, "Ana Hashem Hoshiah Na (Please, G-d, bring us salvation), Ana Hashem Hatzlichah Na (Please, G-d, bring us success)"... On that day (i.e., Hoshana Rabbah) they circled the altar seven times. When they had finished they would say, "Beauty is yours, O altar, beauty is yours." As was done during the week was done on Shabbat (i.e., if Hoshana Rabbah fell on a Shabbat) except (that if it was Shabbat) they would gather them (the aravot) on the eve (of Shabbat) and place them in golden basins so that they would not become wilted.
Why was the rite of the aravah prescribed for Hoshana Rabbah? Sefer ha-Roke'ach answers that the reason is that the aravah grows near water, and on Hoshana Rabbah mankind is judged as regards water.
To commemorate the hakafot (the circling) around the altar, we circle around the Torah scroll on the bimah, for after the destruction of the Bet ha-Mikdash we have nothing left except the Torah and it serves as an altar of atonement. The Hoshana service includes prayers that G-d grant us a year of abundant rain and dew.
Although the Torah does not give this day any special status, the people of Israel have traditionally observed many customs that are particular to this day and invest it with an especially solemn character.
There is a custom from the time of the Prophets Chaggai, Zecharyah, and Malachi to take an aravah, recite a special prayer, and then beat it on the ground. Unlike other Rabbinic obligations, no berachah is recited on this practice since it was enacted as a custom rather than as an obligation.
It is customary to stay awake all night on Hoshana Rabbah and recite the tikkun service, read from the Book of Deuteronomy, recite the entire Book of Psalms, and thus "unite" the night and the day through study and prayer. Those who are especially careful in observing mitzvot immerse themselves in a mikvah before dawn.
Festival clothes are worn, and some have the custom of wearing white clothes as on Yom Kippur, and of lighting the candles which remain from Yom Kippur.
In most Sephardic communities, there is no difference between the text of the prayers on Hoshana Rabbah and the other days of chol ha-mo'ed. In Ashkenazic communities, there are some minor variations, as appear in the Siddur.
After Hallel or after Musaf (customs differ), the Hoshana prayers are recited in the prescribed order, the bimah is encircled seven times, and when the section that begins with the words ta'aneh emunim is reached, the esrog and lulav are put aside and the aravah is taken.
During the chazan's repetition of Musaf, the complete Kedushah is recited instead of the abbreviated version recited on Chol Hamo'ed.
It is customary to eat an especially festive meal. Later in the day, a light snack is eaten and a special prayer is recited after this last act of dwelling in the sukkah.