Reb Levi Yitzchok of Berditchev once observed a simple person dancing with gusto on Simchas Torah. Recognizing that he was utterly unlearned, the Tzaddik asked him what he was rejoicing about. The Yid answered, "When my brother marries off his daughter, should I not participate in his rejoicing?"
The Rebbe explains that in fact Simchas Torah is not a brother's chassunah, a celebration of another Yid, but rather every individual's personal rejoicing. The joy on Simchas Torah is about the essence of the Torah, which is accessible to every Yid, for when he studies even the smallest segment of Torah, through it he is connected to the entire Torah.
Farbrengen.
The 48 hours of Shemini Atzeres and Simchas Torah must be held very precious, for at every moment one can draw pails and barrels full of treasures of Gashmius and Ruchnius. This is accomplished through dancing.