The feast of Sukkot is only seven days long, but the G-d commanded another holy day on the eighth day, called Shemini Atzeret ("eighth assembly"). In the diaspora, Shemini Atzeret is celebrated for two days, with the second day called Simchat Torah ("joy of Torah").
(The commandment for Shemini Atzeret can be found in Leviticus 23:36)
Torah is split up into fifty-four sections, called parashot (singular parshah). Every week, a parshah is read during the week and often the Shabbat message is about that week's parshah. Think of it like the Bible reading tracks that split up all books of the Bible throughout a year. Through the entire year, the entire Bible is covered. This is similar, except for the Torah. Well, except that unlike most of those who take the Bible in a year plan, we don't give up a couple of weeks into February.
Simchat Torah is special because this is the day that we turn the Torah back to the beginning. We've finished the last parshah of Devarim (Deuteronomy) and will continue with the first parshah of the first book in Torah: Beresheet.
Beresheet is the Hebrew word, in English we use the Greek word Genesis. Beresheet literally means "in the beginning," which is nearly the same as the meaning of Genesis. There is a beautiful calming sense to going through the parashot in a year. Every year, even though you've read this parshah multiple times before, you find something newly marvelous. It's like when you watch a mystery movie. The first time, the surprise of the mystery hits you full force and you're shocked. But the second time you watch the movie, you recognize some of the clues leading towards the eventual villain. The third time, you discover more clues. A well-written and directed movie will be layered so well that you can watch it multiple times and not become bored.
The cycle of the parashot also reminds me this wisdom found in Ecclesiastes:
"What has been is what will be,
and what has been done will be done again.
There is nothing new under the sun.
Is there anything about which is said,
'Look! This is new!'?
It was already here long ago,
in the ages long before us."
In the context of the full chapter, it's a bit of a Nihilistic statement. However, these verses give me comfort. Everything has happened before, and it will happen again. There will be no situation I go through that someone hasn't succeed in before. Students of history will recognize the truth in these verses, and they often use this principle to convince scholars to invest in the study of history. If you know the past, you understand the future.
Torah is the study of the history of our faith. There is no Judaism and no Christianity without first Torah. The past found in Torah teaches important lessons that prepare us to advance in the future. What we read in a parshah will occur again, and the solution will have been made plain, over dozens of readings of the same parshah.
On Simchat Torah, we dance with the Torah scroll out of love for its teachings. We rejoice not the monotony of cycling through the parashot, but the opportunity to learn more and grow from starting all over again.