"A mediator, in general, is a person who intervenes between two other persons for the goal of uniting the two parties. The task of the mediator is not to distance further but to reconcile, to bring together the two parties in question.
In the Christian faith, we know that there is only one unique mediator between God and man: the person of Jesus Christ. As St. Paul says: "For there is one God and there is one mediator between God and men, the man Christ Jesus" (1 Tim 2:5). But the perfect mediation of Jesus Christ does not prevent (and in fact provides for) other mediators who are subordinate and secondary to Jesus. Jesus' perfect mediation allows for others to participate in the one and unique mediation of Our Lord. In fact, in the four lines before the passage from 1 Timothy just quoted, St. Paul specifically asks that "supplications, prayers, intercessions, and thanksgivings be made for all men, for kings and all who are in high positions..." and states that doing so is "good, and it is acceptable in the sight of God our Savior, who desires all men to be saved and to come to the knowledge of the truth" (1 Tim 2:1-4). Supplications, prayers, intercessions and thanksgivings made for others are clearly forms of mediation.
We have several examples of secondary mediators in the Old Testament, mediators that were appointed by Almighty God Himself. We have the Old Testament prophets who are inspired by God to mediate between Yahweh and the oftentimes disobedient people of Israel (for the purpose of reconciling Yahweh and Israel). Certainly the patriarchs, like Abraham and Moses, were secondary mediators of the covenant between God and the chosen people of the Old Testament.
In both Old and New Testaments, the glorious mediation of the angels fills the pages of Sacred Scripture as God's special messengers and intercessors; for example, from the Book of Tobit, to the mediation of the Angel Gabriel on behalf of God at the Annunciation (cf. Lk 1:26). St. Thomas Aquinas called the angels "God's secondary causes" since God does so much through the mediation of the angels.
That the one mediation of Jesus Christ is unique, but at the same time allows for the subordinate and secondary mediation of others, is here summarized by St. Thomas Aquinas: "Christ alone is the perfect mediator between God and man...but there is nothing to prevent others in a certain way from being called mediators between God and man in so far as they, by preparing or serving, cooperate in uniting men to God."
Vatican II voices the same truth in these words:
No creature could ever be counted along with the Incarnate Word and Redeemer; but just as the priesthood of Christ is shared in various ways both by his ministers and the faithful, and as the one goodness of God is radiated in different ways among his creatures, so also the unique mediation of the Redeemer does not exclude but rather gives rise to a manifold cooperation which is but a sharing in this one source (Lumen Gentium, No. 62).
Hence, even we, in offering a prayer, or fasting, for a family member or friend, are acting as secondary mediators between God and humanity in the order of spiritual intercession which, rather than detracting from the one mediation of Jesus, in fact, manifests and exercises the power of our one Divine Mediator to the Father.
Theologically, in regards to Mary, the term "mediatrix" refers to a secondary and subordinate female mediator who acts with the same intention as the primary and independent mediator; that is, the reconciliation of individuals. Mary participates in the one mediation of Jesus Christ like no other creature, and hence, she exclusively has the role of "Mediatrix" with Jesus in reconciling humanity with God.
Several scriptural events point to Mary's role as Mediatrix in the order of intercession. It was Mary's intercession at the wedding of Cana (Jn 2:1-11) that led to the first miracle of Our Lord and the beginning of his public ministry. At the Visitation of Mary to Elizabeth, Mary's physical intercession in bringing the unborn Christ to his unborn cousin, John the Baptist, led to John's sanctification in the womb of Elizabeth (cf. Lk 1:41).
This role of Mary as "Mediatrix," or secondary and subordinate mediator with Jesus, has a strong foundation in the apostolic tradition as manifested in this fourth century profession by St. Ephraem (d. 373): "After the Mediator, you (Mary) are the Mediatrix of the whole world."
More recently, Vatican II ends its beautiful treatment of Mary as "Mother in the order of grace" by confirming Mary's role and title as "Mediatrix":
Therefore the Blessed Virgin is invoked in the Church under the titles of Advocate, Helper, Benefactress, and Mediatrix. This, however, is so understood that it neither takes away anything from nor adds anything to the dignity and efficacy of Christ the one Mediator (Lumen Gentium, No. 62).
Pope John Paul II explained Mary's unique and exalted sharing in the one mediation of Jesus in his 1987 encyclical, "Mother of the Redeemer":
Mary entered, in a way all her own, into the one mediation "between God and men" which is the mediation of the man Christ Jesus (1 Tim 2:5). (W)e must say that through this fullness of grace and supernatural life she was especially predisposed to cooperation with Christ, the one Mediator of human salvation. And such cooperation is precisely this mediation subordinated to the mediation of Christ. In Mary's case we have a special and exceptional mediation...(Redemptoris Mater, No. 39).
Mary's role as Mediatrix with Jesus, the one Mediator, has two fundamental expressions in the order of grace. First, Mary uniquely participated with Jesus Christ in reconciling God and man through the Redemption. For this role she has been called "Co-redemptrix" (meaning a secondary and subordinate participator in Jesus' Redemption of the world).
Secondly, Mary gave birth to Jesus, source of all grace, and she distributes all the graces merited by Jesus on Calvary to the human family. This role of Mary as the person responsible for the distribution of graces is referred to as "Dispenser of all graces" or oftentimes by the more general title, "Mediatrix of all graces." "
-By Dr. Mark Miravalle (More info can be found here)