On Tishri 22, the day after the seventh day of Sukkot, is the holiday Shemini Atzeret. In Israel, Shemini Atzeret is also the holiday of Simchat Torah. Outside of Israel, where extra days of holidays are held, only the second day of Shemini Atzeret is Simchat Torah. These two holidays are commonly thought of as part of Sukkot, but that is technically incorrect; Shemini Atzeret is a holiday in its own right and does not involve the special observances of Sukkot.
Shemini Atzeret literally means “the assembly of the eighth (day).” Rabbinic literature explains the holiday this way: G-d is like a host, who invites us as visitors for a limited time, but when the time comes for us to leave, He has enjoyed himself so much that He asks us to stay another day.
The annual cycle of weekly Torah readings is completed at this time. The last Torah portion is read, immediately followed by the first chapter of Genesis, reminding us that the Torah is a circle, and never ends. This completion of the readings is a time of great celebration. There are processions around the synagogue carrying Torahs and plenty of high-spirited singing and dancing. As many people as possible are given the honor of carrying a Torah scroll in these processions. This aspect of the holiday is known as Simchat Torah, which means “Rejoicing in the Torah.” Simchat Torah and Shemini Atzeret are separated in areas that observe an extra day of holidays, so outside of Israel, Shemini Atzeret is Tishri 22 and Simchat Torah is Tishri 23.
In some synagogues, confirmation ceremonies or occasions marking the beginning of a child’s Jewish education are held at this time.
Shemini Atzeret and Simchat Torah are holidays on which work is not permitted.
Source: Judaism 101