Shemini Atzeret falls immediately after the holiday of Succot. Although its name implies that it is part of Sukkot ("Shemini" means eighth, hence implying that the holiday is the eighth day of Sukkot), Shemini Atzeret is actually considered a separate holiday.
Shemini Atzeret is understood as a day highlighting the special relationship between the Jewish people and God. Another explanation focuses on Shemini Atzeret's coming at the end of a particularly rich holiday season. During the Hebrew month of Tishrei we celebrate Rosh Hashana, which is followed ten days later by Yom Kippur. Five days later comes Sukkot. A midrash says that on Shemini Atzeret God says to the Jewish people,"your departure is difficult for me. Stay with me one more day."
The term "Simchat Torah" means "Rejoicing in the Torah". Simchat Torah signifies the completion of the yearly cycle made up of weekly Torah readings. A number of chapters are read each week in the synagogue starting with Parshat Bereshit ( Genesis Ch. 1 ) and after weekly readings completing the reading of the Torah on Simchat Torah. On Simchat Torah, we read the last Torah portion, then proceed immediately to the first chapter of Genesis, reminding us that the Torah is a circle, and never ends.
The completion of the Torah readings is a time of great celebration. There are processions around the synagogue carrying Torah scrolls and plenty of high-spirited singing and dancing with the Torahs. Eveen children are called for an aliyah blessing on Simchat Torah. In addition, as many people as possible are given the honor of carrying a Torah scroll in these processions. Children do not carry the scrolls (they are much too heavy!), but often follow the procession around the synagogue, sometimes carrying small toy Torahs (stuffed plush toys or paper scrolls).