As Pope Saint John Paul II often pointed out, "the comparison Eve-Mary constantly recurs in the course of reflection on the deposit of faith received from divine Revelation. It is one of the themes frequently taken up by the Fathers, ecclesiastical writers and theologians. As a rule, from this comparison there emerges at first sight a difference, a contrast. Eve, as "the mother of all the living" (Gen 3:20), is the witness to the biblical "beginning," which contains the truth about the creation of man made in the image and likeness of God and the truth about original sin. Mary is the witness to the new "beginning" and the "new creation" (cf. 2 Cor 5:17). (Mulieris Dignitatem n.11)
Moreover, Mary, the first redeemed in the history of salvation, is "a new creation:" she is "full of grace" (Ibid.). Mary is the New Eve just as Jesus is the New Adam. This truth so essential to Marian dogma is, in the words of Saint John Henry Newman, "the great rudimental teaching of Antiquity from its earliest date concerning her." (Letter to Pusey)
The Second Vatican Council summarized the question by stating that, "as Saintt Irenaeus says, she ‘being obedient, became the cause of salvation for herself and for the whole human race.’ Hence not a few of the early Fathers gladly assert in their preaching, ‘The knot of Eve's disobedience was untied by Mary's obedience; what the virgin Eve bound through her unbelief, the Virgin Mary loosened by her faith.’ Comparing Mary with Eve, they call her 'the Mother of the living,' and still more often they say: ‘death through Eve, life through Mary’" (Lumen Gentium n. 56).
Saint Irenaeus used the symbol of a reverse circuit to describe how the evil contracted in the origins was overcome: Christ assumed the figure of Adam, the cross stood for the tree of the fall, and Mary assumed the figure of Eve. Each of the elements that were corrupted by the fall were renewed from their roots. In the 12th century, the title of "New Eve" was attached to Mary's spiritual motherhood because of this notion of "recirculatio" (circuit in reverse).
Adapted from: Aleteia