The first of the year is a solemnity in honor of Mary, Mother of God. I imagine this is to remind us to put the New Year ~ along with all our concerns and desires ~ in her hands.
Two simple ways to honor Mary in the midst of all our New Year celebrations:
1. When saying grace, add a Hail Mary.
2. Before your meal, say a toast in her honor. We said this at dinner, "Mary, Mother of God, be our Mother in the New Year."