January 1 is the feast of Mary, the Mother of God.
This title was officially given to Mary at the Council of Ephesus in 431. A bishop named Nestorius, who was patriarch of Constantinople, had been teaching false ideas about Jesus. Nestorius said that Jesus was, in effect, two persons, a human person and a divine person. This is different from the Church's teaching that Jesus is one person, the divine person, with two natures: human and divine.
A consequence of Nestorius' teaching is that Mary can't be the Mother of God, but only of the human Jesus.
The ordinary Catholics of his day may not have followed the theological subtleties of the debate, but they knew that they had always honored Mary as the Mother of God, and whoever denied that had to be wrong. After the bishops at the Council of Ephesus declared Mary is truly the Mother of God, the faithful to the streets and had a great procession in her honor.
This shows how what the Church teaches about Mary is important because it safeguards the true teaching about Jesus.