Catechism of the Catholic Church
1362 The Eucharist is the memorial of Christ's Passover, the making present and the sacramental offering of his unique sacrifice, in the liturgy of the Church which is his Body. In all the Eucharistic Prayers we find after the words of institution a prayer called the anamnesis or memorial.
1363 In the sense of Sacred Scripture the memorial is not merely the recollection of past events but the proclamation of the mighty works wrought by God for men. 184 In the liturgical celebration of these events, they become in a certain way present and real. This is how Israel understands its liberation from Egypt: every time Passover is celebrated, the Exodus events are made present to the memory of believers so that they may conform their lives to them.
1364 In the New Testament, the memorial takes on new meaning. When the Church celebrates the Eucharist, she commemorates Christ's Passover, and it is made present the sacrifice Christ offered once for all on the cross remains ever present. 185 "As often as the sacrifice of the Cross by which 'Christ our Pasch has been sacrificed' is celebrated on the altar, the work of our redemption is carried out." 186
1365 Because it is the memorial of Christ's Passover, the Eucharist is also a sacrifice. The sacrificial character of the Eucharist is manifested in the very words of institution: "This is my body which is given for you" and "This cup which is poured out for you is the New Covenant in my blood." 187 In the Eucharist Christ gives us the very body which he gave up for us on the cross, the very blood which he "poured out for many for the forgiveness of sins." 188
1366 The Eucharist is thus a sacrifice because it re-presents (makes present) the sacrifice of the cross, because it is its memorial and because it applies its fruit:
[Christ], our Lord and God, was once and for all to offer himself to God the Father by his death on the altar of the cross, to accomplish there an everlasting redemption. But because his priesthood was not to end with his death, at the Last Supper "on the night when he was betrayed," [he wanted] to leave to his beloved spouse the Church a visible sacrifice (as the nature of man demands) by which the bloody sacrifice which he was to accomplish once for all on the cross would be re-presented, its memory perpetuated until the end of the world, and its salutary power be applied to the forgiveness of the sins we daily commit. 189
1367 The sacrifice of Christ and the sacrifice of the Eucharist are one single sacrifice: "The victim is one and the same: the same now offers through the ministry of priests, who then offered himself on the cross; only the manner of offering is different." "And since in this divine sacrifice which is celebrated in the Mass, the same Christ who offered himself once in a bloody manner on the altar of the cross is contained and offered in an unbloody manner. . . this sacrifice is truly propitiatory." 190
1368 The Eucharist is also the sacrifice of the Church. The Church which is the Body of Christ participates in the offering of her Head. With him, she herself is offered whole and entire. She unites herself to his intercession with the Father for all men. In the Eucharist the sacrifice of Christ becomes also the sacrifice of the members of his Body. The lives of the faithful, their praise, sufferings, prayer, and work, are united with those of Christ and with his total offering, and so acquire a new value. Christ's sacrifice present on the altar makes it possible for all generations of Christians to be united with his offering.
In the catacombs the Church is often represented as a woman in prayer, arms outstretched in the praying position. Like Christ who stretched out his arms on the cross, through him, with him, and in him, she offers herself and intercedes for all men.
1369 The whole Church is united with the offering and intercession of Christ. Since he has the ministry of Peter in the Church, the Pope is associated with every celebration of the Eucharist, wherein he is named as the sign and servant of the unity of the universal Church. The bishop of the place is always responsible for the Eucharist, even when a priest presides; the bishop's name is mentioned to signify his presidency over the particular Church, in the midst of his presbyterium and with the assistance of deacons. The community intercedes also for all ministers who, for it and with it, offer the Eucharistic sacrifice:
Let only that Eucharist be regarded as legitimate, which is celebrated under [the presidency of] the bishop or him to whom he has entrusted it. 191
Through the ministry of priests the spiritual sacrifice of the faithful is completed in union with the sacrifice of Christ the only Mediator, which in the Eucharist is offered through the priests' hands in the name of the whole Church in an unbloody and sacramental manner until the Lord himself comes. 192
1370 To the offering of Christ are united not only the members still here on earth, but also those already in the glory of heaven. In communion with and commemorating the Blessed Virgin Mary and all the saints, the Church offers the Eucharistic sacrifice. In the Eucharist the Church is as it were at the foot of the cross with Mary, united with the offering and intercession of Christ.
1371 The Eucharistic sacrifice is also offered for the faithful departed who "have died in Christ but are not yet wholly purified," 193 so that they may be able to enter into the light and peace of Christ:
Put this body anywhere! Don't trouble yourselves about it! I simply ask you to remember me at the Lord's altar wherever you are. 194
Then, we pray [in the anaphora] for the holy fathers and bishops who have fallen asleep, and in general for all who have fallen asleep before us, in the belief that it is a great benefit to the souls on whose behalf the supplication is offered, while the holy and tremendous Victim is present.... By offering to God our supplications for those who have fallen asleep, if they have sinned, we . . . offer Christ sacrificed for the sins of all, and so render favorable, for them and for us, the God who loves man. 195
1372 St. Augustine admirably summed up this doctrine that moves us to an ever more complete participation in our Redeemer's sacrifice which we celebrate in the Eucharist:
This wholly redeemed city, the assembly and society of the saints, is offered to God as a universal sacrifice by the high priest who in the form of a slave went so far as to offer himself for us in his Passion, to make us the Body of so great a head.... Such is the sacrifice of Christians: "we who are many are one Body in Christ" The Church continues to reproduce this sacrifice in the sacrament of the altar so well-known to believers wherein it is evident to them that in what she offers she herself is offered. 196
English Translation of the Cathechism of the Catholic Church for the United States of America © 1997, United States Catholic Conference, Inc.