For [the] seven days [of Sukkot] you shall bring a fire offering to G‑d. On the eighth day, it shall be a holy convocation for you... It is a [day of] detention.

Leviticus 23:36

[G‑d says to Israel,] "I have detained you [to remain] with Me." This is analogous to a king who invited his sons to feast with him for a certain number of days, and when the time came for them to leave, he said: "My sons! Please, stay with me just one more day; it is difficult for me to part with you!"

Rashi's commentary ad loc

After the seven-day holiday of Sukkot, we celebrate an independent one-day holiday, called "Shemini Atzeret." Outside of Israel, as is the case with almost all Biblical holidays, an extra day is added to this holiday (see Why are holidays celebrated an extra day in the Diaspora?), and this day is known as "Simchat Torah." Although this holiday directly follows Sukkot, it is not actually part of Sukkot.1

Integral to all the festivals on the Jewish calendar – Passover, Shavuot, and Sukkot – is the mitzvah to rejoice. "Rejoice on your festivals!" the Torah enjoins us.2 Of all the festivals, however, only Sukkot is described as "the season of our rejoicing,"3 because the joy of Sukkot eclipses the joy of the other festivals (as evidenced by Sukkot's nightly "Water Drawing Celebrations").

And then there's the utterly unbridled joy of Shemini Atzeret and Simchat Torah, which surpasses even the joy of Sukkot.

Historically (in 1313 BCE, 2449 years since Creation), on Yom Kippur, G‑d forgave the Jewish nation for the sin of the Golden Calf, and then, on the very same day, Moses descended from Mount Sinai with the second tablets, the symbol of G‑d's acceptance of the Jews' teshuvah (repentance).It is time to celebrate the atonement we've attained Every year on Yom Kippur we attempt to recapture the spirit of atonement which is present on that day. As such, a somber atmosphere prevails as we fast, pray, repent, and beseech G‑d for forgiveness. A week and a half later, it is time to celebrate the atonement we've attained, time to rejoice with the second tablets. And the joy produced by reaching inwards, overcoming obstacles, and reconnecting to our essential core which remained faithful to G‑d throughout, is absolutely unparalleled. (See Hidden and Revealed for more on this topic.)

The two days of Shemini Atzeret and Simchat Torah are very precious. Rabbi Shalom DovBer Schneersohn, fifth Rebbe of Chabad-Lubavitch, stated:

The 48 hours of Shemini Atzeret and Simchat Torah should be highly treasured. Every moment is an opportunity to draw bucket- and barrelfuls of material and spiritual treasures. And this is accomplished through dancing...4

Simchat Torah and Shemini Atzeret

Outside the Land of Israel, where (as mentioned before) festivals are observed for two days, the two days of this holiday are quite distinct from each other (unlike other two-day holidays where, as a rule, the second day is more or less a simple repeat of the first).

The first day, known as Shemini Atzeret, is reserved for the joy of the festival and for the prayers for rain (see Shemini Atzeret Guide). Yizkor is recited on this day, and, as will soon be explained, we eat in the sukkah.

The second day, Simchat Torah, is reserved for the celebration of the conclusion of the cycle of reading from the Torah. The highlight of this day are the hakafot (see Hakafot), held both on the eve and morning of Simchat Torah, in which we march and dance with Torah scrolls around the reading table in the synagogue. (Chassidic communities – Chabad included – have the custom of conducting hakafot also on Shemini Atzeret at night.)

Eating in the Sukkah on Shemini Atzeret

The fact that outside of Israel every holiday is celebrated for an extra day presents a problem on Sukkot—because it is immediately followed by another holiday, Shemini Atzeret. It would be disrespectful to Shemini Atzeret – which is a holiday in its own right, with its own laws, customs, and theme – for us to also be celebrating Sukkot on the same day. Just imagine how you'd feel if someone invited to your wedding decided to bring along his son to celebrate his Bar Mitzvah...

Therefore, we don't celebrate Sukkot on Shemini Atzeret.We can argue that we are simply enjoying the Shemini Atzeret holiday meal al fresco We don't take the Four Kinds on Shemini Atzeret, and we don't mention Sukkot in the day's prayers. The exception to this rule, however, is sitting in the sukkah. Doing so doesn't disturb the holiday of Shemini Atzeret, since we can argue that we are simply enjoying the Shemini Atzeret holiday meal al fresco, savoring the breeze in the cool shade of the sukkah. Normative halachah (Jewish law) therefore requires eating in the sukkah5 on Shemini Atzeret.6 We do not, however, recite the blessing for sitting in the sukkah,7 for that would be a blatant indication that we are still in Sukkot mode.

In Israel

In the Land of Israel, both these holidays, Shemini Atzeret and Simchat Torah, are celebrated simultaneously on the same day. As such, all the customs of Simchat Torah are observed together with those of Shemini Atzeret. (There's also no eating in the sukkah on this day in Israel, for the reason to eat in the sukkah is in consideration of the extra "Diaspora day" of the holiday of Sukkot.)

Following the custom of the holy Arizal, many in Israel participate in hakafot sh'niyot ("second hakafot") on the night following the one-day holiday—thus joining their Diaspora brothers and sisters in their celebration of the Torah. These second hakafot have an advantage: since it is no longer a holiday, the singing can be accompanied by live music. If you are in Israel for the holiday, you might want to make your way on this night to the Western Wall, where the singing and dancing lasts well into the night.