According to our tradition, the Torah was given on the 6th of Sivan, the day on which we observe the holiday of Shavuot, but only received by Am Yisrael on the 7th of Sivan. By celebrating Shavuot on the day of the giving of the Torah rather than on the day of its reception (which we essentially celebrate every day when we learn Torah) we reconnect our Torah with the voice of God.