To put it simply:
Mary is the mother of Jesus (we all acknowledge that).
Jesus is God (all Christians believe this).
Therefore, Mary is the mother of God (insofar as Jesus, her son, is God).
We believe that Mary is the creature whom God, in His ineffable mercy and goodness, honored above all others by making her His mother at the Incarnation.She is also the Mother of God because her virginal motherhood directly depends on and belongs to God in an absolutely unique way. Her Son is God and her motherhood is a gift from and belongs to God alone, though God has subsequently given her motherhood to the whole church as one of the means to help us to approach Him in His ineffable essence, which far surpasses all that we can imagine. So she is, in accordance with the inscrutable and irreproachable will of God, our mother too.