The members of the Mystical Body are nourished by the Sacraments

From Pope Pius XII’s encyclical Mystici Corporis Christi (1943):

Now we see that the human body is given the proper means to provide for its own life, health and growth, and for that of all its members. Similarly, the Savior of mankind out of His infinite goodness has provided in a wonderful way for His Mystical Body, endowing it with the Sacraments, so that, as though by an uninterrupted series of graces, its members should be sustained from birth to death, and that generous provision might be made for the social needs of the Church. Through the waters of Baptism those who are born into this world dead in sin are not only born again and made members of the Church, but being stamped with a spiritual seal they become able and fit to receive the other Sacraments. By the chrism of Confirmation, the faithful are given added strength to protect and defend the Church, their Mother, and the faith she has given them. In the Sacrament of Penance a saving medicine is offered for the members of the Church who have fallen into sin, not only to provide for their own health, but to remove from other members of the Mystical Body all danger of contagion, or rather to afford them an incentive to virtue, and the example of a virtuous act.

Nor is that all; for in the Holy Eucharist the faithful are nourished and strengthened at the same banquet and by a divine, ineffable bond are united with each other and with the Divine Head of the whole Body. Finally, like a devoted mother, the Church is at the bedside of those who are sick unto death; and if it be not always God’s will that by the holy anointing she restore health to the mortal body, nevertheless she administers spiritual medicine to the wounded soul and sends new citizens to heaven—to be her new advocates—who will enjoy forever the happiness of God.

Mystici Corporis Christi 18-19

In persona Christi

From the foreword by the late Fr. Benedict J. Groeschel CFR to Dr. Scott Hahn’s The Lamb’s Supper: The Mass as Heaven on Earth (Doubleday, 1999):

I always feel a twinge of annoyance when I see in a college or a hotel a list of “religious services” and observe the Mass listed at 9 am. The Mass is not a religious service. When Catholics say morning prayer or the recitation of the rosary or even have Benediction of the Blessed Sacrament, that’s a service. It’s something that we do for God, similar to the public prayer of any religious denomination. But the Holy Sacrifice of the Eucharist, the Divine Liturgy, is not precisely — in its essence — done by man at all.

Let me tell you, I’ve been a priest for forty years and I never conducted a “service” called a Mass. I was a “stand-in” for the High Priest, to use the words of Church teaching, I was there functioning in persona Christi — in the person of Christ, the High Priest of the Epistle to the Hebrews. People do not come to Mass to receive my body and blood, and I could not have given it to them if they did. They come for communion with Christ.

This is the mysterious element in all Christian sacraments — including baptism. For this reason, in case of great necessity anyone can function in persona Christi to give baptism, because it is Christ Who actually baptizes. It is Christ Who forgives sin, Christ Who prepares the dying, Christ Who ordains and Who blesses the marriages.

Like Catholic and Orthodox Christians who think about it (as well as some Anglicans and even some Lutherans), I believe that Christ is the Priest of all the sacraments, just as He speaks to us from every page of Sacred Scripture. He ministers to us in every sacrament — and we experience in this way the vitality of His mystical body.