On the first day of Sivan 2448, the third month after Nisan, in which the Israelites had left the land of Egypt they came to the Sinai Desert, where G-d told them He would give them the Torah. The anticipation they felt on this day over receiving the Torah is to be re-experienced daily, for we are to relate to the Torah as if G-d gives it anew every day.
The Torah was given specifically in the third month, for the number three symbolizes the threefold unity the Torah creates.
"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. It 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.
—From the Kehot Chumash