From the Rebbe’s explanations:
– A presumption (chazakah) is established only when it occurs three times. (B. Metzia 106b). Thus, the holiday of Sukkos is firmly set and strengthened (the meaning of chazakah) with the onset of the third day.
… The number “three” also has a connection to a gathering of many Jews. “Three” indicates peace and unity. “One” has no adversary, “two” oppose each other and the third makes peace. This is true of the heavenly peace which G‑d invokes upon the angels, Michael and Gavriel, as well as the peace of the three-member Bais Din which can make a definitive ruling in Halachah; only because there are three judges. When many Jews gather in unison we see that despite their differences they can be united. This is the power of three.
From the Rebbe’s talk on the 3rd Night of Sukkos, 5746.