"Mother of God," Theotokos, is the title that was officially attributed to the Virgin Mary in the fifth century, to be exact, at the Council of Ephesus in 431, but which had already taken root in the devotion of the Christian people since the third century, in the context of the heated discussions on the Person of Christ in that period. This title highlights the fact that Christ is God and truly was born of Mary as a man. In this way His unity as true God and true man is preserved. Actually however much the debate might seem to focus on Mary, it essentially concerned with the Son.
Desiring to safeguard the full humanity of Jesus, several Fathers suggested a weaker term: instead of the title Theotokos, they suggested Christotokos, "Mother of Christ." However, this was rightly seen as a threat to the doctrine of the full unity of Christ's divinity with His humanity. On the one hand, therefore, after lengthy discussion at the Council of Ephesus in 431, as I said, the unity of the two natures—the divine and the human (cf. DS, n. 250)—in the Person of the Son of God was solemnly confirmed and, on the other, the legitimacy of the attribution of the title Theotokos, Mother of God, to the Virgin (ibid., n. 251).
After this Council a true explosion of Marian devotion was recorded and many churches dedicated to the Mother of God were built. Outstanding among these is the Basilica of St Mary Major here in Rome. The teaching on Mary, Mother of God, received further confirmation at the Council of Chalcedon (451), at which Christ was declared "true God and true man... born for us and for our salvation of Mary, Virgin and Mother of God, in His humanity" (DS, n. 301). As is well known, the Second Vatican Council gathered the teachings on Mary in the eighth chapter of the Dogmatic Constitution on the Church Lumen Gentium, reaffirming her divine motherhood. The chapter is entitled "The Blessed Virgin Mary, Mother of God, in the Mystery of Christ and the Church."
Benedict XVI – General Audience of January 2, 2008 (excerpt)