What is Simchat Torah?
The holiday of Simchat Torah is a great invention of the Jewish People in their Exile. It celebrates the completion of and the beginning of the "Reading of the Torah."
What do you mean "invention?"
Since the Shmini Atzeret-Simchat Torah Holiday has no intrinsic Mitzvot, but is a celebration of the relationship between G-d and Israel, the Jewish People created a "Mitzvah," so to speak, which brought out and emphasized that relationship, which is based on the Torah.
What does "Reading of the Torah" mean?
This expression refers to the fact that Moshe had instituted the public reading of the Torah on each Shabbat. Much later generations defined the schedule such that the reading of the entire Torah would be completed on Simchat Torah and begun again that very day.
How is the completion-and-beginning celebrated?
On the night of the Holiday, the celebration is begun with the reading of a selection of verses, beginning "Ata Horayta," "You have been Shown," recounting how G-d revealed Himself to the Jewish People at Mt. Sinai, declaring G-d's uniqueness, and emphasizing our reliance upon Him to bring our final redemption. Then all eyes turn to the Ark, which contains the "Sifrei Torah," the actual Scrolls of the Torah. The Ark is opened and all the Scrolls are taken out, and everybody in the shul is given an opportunity to dance with them.