Mary is the mother of Jesus Christ, who is God and man.  She is therefore the Mother of God.  This is a dogma of the faith accepted as such from the earliest times, as is evident from countless expressions of the Fathers, and it was defined by the Council of Ephesus in 431.  It does not mean, of course, that Mary generated the Godhead, any more than an ordinary mother generates her son’s soul.  It means simply that she is the mother of a Person who is God.
This is her fundamental dignity, and the origin and justification of all the honour which Catholics pay to her.


Council of Ephesus, 431 A.D.

Pope St. Celestine I (422-432 A.D.)

This expression, however, “the Word was made flesh,” can mean nothing else but that he partook of flesh and blood like to us; he made our body his own, and came forth man from a woman, not casting off his existence as God, or his generation of God the Father, but even in taking to himself flesh remaining what he was. This the declaration of the correct faith proclaims everywhere. This was the sentiment of the holy Fathers; therefore they ventured to call the holy Virgin, the Mother of God, not as if the nature of the Word or his divinity had its beginning from the holy Virgin, but because of her was born that holy body with a rational soul, to which the Word being personally united is said to be born according to the flesh.

And since the holy Virgin brought forth corporally God made one with flesh according to nature, for this reason we also call her Mother of God, not as if the nature of the Word had the beginning of its existence from the flesh.
If anyone will not confess that the Emmanuel is very God, and that therefore the Holy Virgin is the Mother of God, inasmuch as in the flesh she bore the Word of God made flesh (as it is written, “The Word was made flesh”) let him be anathema.

The Catholic Encyclopedia

Mary’s Divine motherhood

Mary’s Divine motherhood is based on the teaching of the Gospels, on the writings of the Fathers, and on the express definition of the Church.   St. Matthew (1:25) testifies that Mary “brought forth her first-born son” and that He was called Jesus. According to St. John (1:15) Jesus is the Word made flesh, the Word Who assumed human nature in the womb of Mary. As Mary was truly the mother of Jesus, and as Jesus was truly God from the first moment of His conception, Mary is truly the mother of God. Even the earliest Fathers did not hesitate to draw this conclusion as may be seen in the writings of St. Ignatius, St. Irenaeus, and Tertullian. The contention of Nestorius denying to Mary the title “Mother of God” was followed by the teaching of the Council of Ephesus proclaiming Mary to be Theotokos in the true sense of the word.

FROM - http://www.calefactory.org/misc-mary-motherofgod.htm