The title "Mother of God" is not found as such in the writings of the New Testament. The first known mention is that of Saint Hippolytus of Rome (d. 235). Later, Nestorius, Patriarch of Constantinople (428), will dispute the attribution of this title to Mary because of his views on Christology. For him, the Son of God is one thing, the son of Mary another, in the sense that he sees in Christ two Persons: one Divine (the Logos), the other human (Jesus). Consequently for Nestorius, Mary cannot be called "theotokos" (Mother of God), at least in the real sense demanded by the hypostatic union (the union of two natures, the human and the Divine, in the one Person of the Word).
The Council of Ephesus (431) defends this unicity of person in Christ and condemns Nestorius and his followers. It approves, by acclamation, the second letter of Saint Cyril to Nestorius and through this approval officially confirms the attribution to Mary of the title Mother of God. The normative decision taken at Ephesus will be explicitly promulgated as dogma in 451 by the Council of Chalcedon.
Thus, the title of Mother of God derives from Catholic teaching on the Incarnation of the Word. Mary conceives and brings forth, in His human nature, One Who is God from all eternity. Jesus is not God by the fact that He is conceived or born of Mary (this would not be a Mystery but an absurdity because it would make Mary mother of the Divine nature). Mary is Mother of God because from her own flesh she gives to the Word a human nature like hers. And just as in ordinary human generation the truth of the parents' generative action is not the human nature produced but the person subsisting in this nature, so in the case of Mary: her maternal action reaches to the Person of the Word, Who by this very fact is truly her Son. Mary is "theotokos" because "the Word was made flesh" in her and through her.