The Eucharist is a sacrifice, not a commemorative meal. It is not a new sacrifice, but a memorial of Christ’s Passover, a renewal of the one and only perfect sacrifice of Jesus. At the Eucharist the offering of Christ’s Body and Blood are re-presented to us in a unique way. At the moment of the Consecration, we are brought back to Calvary and Calvary is brought forward to us. One sacrifice, always present in eternity outside of time, re-presented to us in our space and time on the altar.
This is a difficult concept to understand. Think about the grace a person receives during Baptism. This grace is not new, it is always present in Heaven with God, but it is renewed every time an individual is baptized. The same grace applied individually to each person during their baptism.
Ok, something less esoteric. What happens to the television signal when you turn off your TV? The signal is always present, still broadcasting from the station, even when your television is off. Turn your television back on and the picture appears, the signal has been renewed in your TV, but not to the station.
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. The priesthood of Jesus is eternal and unchangeable, “because he remains forever, [he] has a priesthood that does not pass away. Therefore, he is always able to save those who approach God through him since he lives forever to make intercession for them.”
Jesus, in his own words at the Last Supper instituted the sacrificial character of the Eucharist when he said, “This is my blood of the covenant, which will be shed on behalf of many for the forgiveness of sins.” In the Eucharist the same body and blood that Christ gave up for us on the cross is made present. There is no redemption without the shedding of blood, but in the divine sacrifice of the Mass, the same Christ who offered himself once in a bloody manner on the altar of the cross is contained and is offered in an unbloody manner.
So by the Word of Christ and the action of the Holy Spirit, the Eucharist is an unbloody sacrifice making present the eternal sacrifice of Christ on the cross memorialized eternally for the forgiveness of the sins we daily commit. Or as the Catechism of the Catholic Church and the Council of Trent declare:
“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 in his sinfulness 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.”
 CCC 1364 Hebrews 7:24-25 Matthew 26:28 CCC1365 Hebrews 9:27 CCC 1367, Council of Trent (1562), Hebrews 9:14
 CCC 1367, Council of Trent (1562), 1 Cor 11:23, Hebrews 7:24, 27