"We never give more honour to Jesus than when we honour His Mother, and we honour her simply and solely to honour Him all the more perfectly. We go to her only as a way leading to the goal we seek - Jesus, her Son." - St. Louis Marie de Montfort
Having just celebrated the Nativity the Church concludes the octave of Christmas by honoring Mary under her greatest title, the Mother of God. Upon the fact of her divine Motherhood depends all her dignities and prerogatives.
The Catechism of the Catholic Church (paragraph 509) teaches, “Mary is truly ‘Mother of God’ since she is the mother of the eternal Son of God made man, who is God himself.”
The solemnity of Mary, Mother of God, is a holy day of obligation, and we celebrate this feast every year on January 1 in honor of her.
The Catechism of the Catholic Church (paragraph 495) teaches,
Called in the Gospels "the mother of Jesus," Mary is acclaimed by Elizabeth, at the prompting of the Spirit and even before the birth of her son, as "the mother of my Lord." In fact, the One whom she conceived as man by the Holy Spirit, who truly became her Son according to the flesh, was none other than the Father's eternal Son, the second person of the Holy Trinity. Hence the Church confesses that Mary is truly "Mother of God" (Theotokos).
She was declared the Mother of God (Theotokos) in 431 AD at the Council of Ephesus.
The Gospels teach that He whom we call Jesus Christ was true God and true man (Jn. 1:14). St. John tells us that “the Word became flesh and dwelt among us” (Jn. 1:14), and thus of the Church. St. Ignatius of Antioch, on his way to his martyrdom in Rome in 107 A.D., wrote to the Ephesians insisting on it,
“For our God, Jesus Christ, was, according to the appointment of God, conceived in the womb by Mary, of the seed of David, but by the Holy Spirit” (Ignatius, Eph. 18)
As with most Church dogmas, the teaching is already present in Revelation, enters ordinary teaching, but becomes a dogma only when there is serious opposition to believing it, or error in expressing it. In this case, the Council of Ephesus declared the dogma in 431, to settle the Christological controversy created by Nestorius.