On the first day of Sivan 2448, the third month after Nissan, in which the Israelites had left Egypt, they came to the Sinai Desert, on this day.
The Torah was given specifically in the third month, for the number three symbolizes the threefold unity created by the Torah.
"One" obviously represents unity--there is no separate entity to dissent or disagree--but it is an inherent unity, not a created one. The only true unity of this sort is G-d's; He was, is, and will be one, for there is in truth nothing other than Him.
"Two" signifies the duality, discord, and separation we experience within G-d's world, the constant dichotomy of body and soul, physical and spiritual, and good and evil.
"Three" introduces a third element that reconciles and unites these discordant concepts. This element does not choose one way or the other, for that would be returning to one, the duality of two combatants no longer existing. Rather, it blends the two; it allows each its own individuality and yet enables them at the same time to fuse into a greater whole.
The Torah was given, says Maimonides, to bring peace into the world. Through the Torah, G-d allows His infinite wisdom to be distilled into a form accessible by finite creatures. He thus gave humanity the capacity to bring G-dliness into the world, to continue to exist as finite human beings and still attain a level of Divine consciousness. The Torah does not superimpose one reality in place of the other, but rather melds the two into a G-dly and meaningful existence in the context of this world.
Chumash Synagogue Edition