In the first ages of the Church the day sacred to our Blessed Lady, under her great title of Mother of God, was January 1. Evident traces of this devotion remain in the liturgy proper to the feast of the Circumcision, which is now kept on that day. Many churches having petitioned for a special festival in honor of Our Lady’s divine maternity, a day, usually in the month of October, was granted by the Holy See for its celebration. By a decree of the Sacred Congregation of Rites, April 24, 1914, the eleventh of October was assigned. Pius IX raised it to a double of the second class and extended it to the Universal Church.
All Catholics believe that Mary is the Mother of God. This does not mean that she is not a creature of God, nor that God did not exist before she was created. It means that He who was her Son was a Divine Person. In Christ there are two natures: the nature of God and the nature of man; but in Him there is only one Person, a Divine Person, the Second Person of the Blessed Trinity. Hence all that may be predicated of either nature many with propriety be said of the Savior in the concrete form, without distinguishing the two natures. So we may say that God was born of the Blessed Virgin Mary. We then refer to the Person of the Son of God. Who is both God and Man. Christ, Who is God, was born according to His human nature of the Blessed Virgin. She is, therefore, truly the Mother of God.
(Source: The New Roman Missal, Rev. F. X. Lasance)