What is "Shmini Atzeret?"
"Shmini Atzeret" is the holiday which is celebrated on the eighth day counting from the beginning of "Sukkot." In Israel, it is celebrated for one day, which is a combination of "Shmini Atzeret" and "Simchat Torah." In the Diaspora, "Shmini Atzeret" and "Simchat Torah" are separated, with "Shmini Atzeret" being celebrated on the eighth day, and "Simchat Torah" being on the ninth day.
Is Shmini Atzeret part of Sukkot?
Even though its celebration is keyed to the beginning of Sukkot, Shmini Atzeret is a separate holiday. Because it is considered as separate from Sukkot, the blessing of "Shehecheyanu(1)" is recited - the wife, when she lights the candles ushering in the Holiday and the husband, when he recites the Kiddush at the evening Seudah (festive meal).
What does the name "Shmini Atzeret" mean?
"Shmini" means the eighth; in general, the number eight symbolizes perfection, as it does in the case of "brit milah," the covenant of circumcision. The brit is performed on the eighth day to "complete," as it were, or to instill the potential for perfection, in the human being.
"Atzeret" means "holding back," or that which is held back for the purpose of bringing it to its state of completion. Thus, the name "Shmini Atzeret" means the eighth day which is the additional day that brings the seven-day holiday of Sukkot to its state of perfection.
1. The classic time that the blessing "Blessed are you, Our G-d, King of the Universe, Who has kept us alive ("Shehecheyanu"), and in existence, and brought us to this time" is recited is at the beginning of a festival. If Shmini Atzeret were merely the conclusion of Sukkot, this blessing would not be recited
The "Real" Atzeret
What is the "Real" Atzeret?
The name "Atzeret" is actually used most in the Talmud to refer to the holiday of Shavuot. Shavuot can be seen as the "completion" of Pesach - for Pesach, commemorating the Exodus, represents our "physical" birth as a nation, while Shavuot, commemorating our receiving of the Torah, represents our "spiritual" birth. Similarly, the holiday of Sukkot is replete with "physical" Mitzvot: the Sukkah itself, the Lulav and Esrog, the Hadassah and Aravah - but on Shmini Atzeret, all those commandments are removed, and all that remains is the spiritual component, the relationship with Hashem.
Shmini Atzeret should really have been placed seven weeks after Sukkot as Shavuot, the "closure" of Pesach, follows it by seven weeks, but, according to the Midrash, Hashem had mercy on the Jewish People. For Pesach is in the Spring and Shavuot is in the Summer, both pleasant times for travel (these holidays are all "Regalim," Pilgrim Festivals, on which Jewish males are obligated to travel to the Temple in Yerushalayim), but seven weeks after Sukkot would already be into the rainy season in Israel, and travel would not be pleasant then. Therefore, Hashem allowed the closure of Sukkot, Shmini Atzeret, to be celebrated right after Sukkot.
Further evidence that Shmini Atzeret is the closure of Sukkot is provided by the Midrash's interpretation of the sacrifices brought on the two holidays.
Over the course of the seven days of Sukkot, seventy bulls are brought, beginning with thirteen on the first day and seven on the last. These are interpreted as being for the benefit of all the nations of the world.
But on Shmini Atzeret, G-d says to the Jewish People, "All the guests have gone home now. Stay with me yet another day, and we will celebrate together, just you and I."