"The Mass makes present the sacrifice of the Cross"

I find that post-Vatican II Catholics tend to be shocked when this aspect of the Mass is pointed out to them.  Poor catechesis is partly to blame, but not entirely.  The following words are taken from F.J. Sheed's "Theology for Beginners." :


The Sacrifice of the Mass
Upon Calvary Christ Our Lord offered himself in sacrifice for the redemption of the human race. There had been sacrifices before Calvary, myriads of them—foreshadowings, figures, distortions often enough, but reaching out strongly or feebly towards the perfection of Calvary's sacrifice.
These represented an awareness in men, a sort of instinct, that they must from time to time take something out of that vast store of things God has given them and give it back to him. Men might have used the thing for themselves but chose not to; they offered it to God, made it sacred (that is what the word sacrifice means). In itself, sacrifice is simply the admission that all things are God's; even in a sinless world this would be true, and men would want to utter the trust by sacrifice. With sin, there was a new element; sacrifice would include the destruction of the thing offered—an animal, usually.
We can study these sacrifices, as they were before Calvary at once perfected and ended them, in the Temple sacrifices of the Jews, the Chosen People. The whole air of the Old Testament is heavy with the odor of animals slain and offered to God. The slaying and the offering—immolation and oblation—were both necessary elements. But whereas the offering was always made by the priests, the slaying need not be done by them; often it was the work of the Temple servants. For it was not the slaying that made the object sacred, but the offering. The essential thing was that the priest offer a living thing slain.
With Christ, we have said, sacrifice came to its perfection. The priest was perfect, for Christ was the priest. The victim was perfect, for he was the victim too. He offered himself, slain. But not slain by himself. He was slain by others, slain indeed by his enemies.
What he did was complete, once for all, not to be repeated. It accomplished three things principally—atoned for the sin of the race, healed the breach between the race and God, opened heaven to man, opened it never to be closed. His is "the propitiation for our sins, and not for ours only but for those of the whole world" (1 Jn 2:1).
With such completion, what was still to be done? For something was still to be done. Christ is still in action on men's behalf, as the Epistle to the Hebrews tells us. Jesus has entered "into heaven itself, that he may appear now, in the presence of God for us" (9:24). He is "always living to make intercession for us" (7:25). What still remains to be done is not an addition to what was done on Calvary, but its application to each man—that each of us should receive for himself what Our Lord won for our race.
The "intercession" just spoken of is not a new sacrifice but the showing to God of the sacrifice of Calvary. The Victim, once slain, now deathless, stands before God, with the marks of the slaying still upon him—"a Lamb standing, as it were slain" (Rv 5:6).
We are now in a better position to understand the Sacrifice of the Mass. In heaven Christ is presenting himself, once slain upon Calvary, to his heavenly Father. On earth the priest—by Christ's command, in Christ's name, by Christ's power—is offering to God the Victim once slain upon Calvary. Nor does this mean a new sacrifice, but Calvary's sacrifice presented anew—in order that the redemption won for our race should produce its fruit in us individually.
In the Mass the priest consecrates bread and wine, so that they become Christ's body and blood. Thus the Christ he offers is truly there really there. The Church sees the separate consecration as belonging to the very essence of the Mass. It is a remainder of Christ's death—and he had told his first priests at the Last Supper that, in doing what he had just done, "they should show forth the death of the Lord, until he come (1 Cor 11:26). They should show forth Christ's death, remind us of his death, not, of course, kill him, any more than he had killed himself on Calvary.
The priest offers the sacrifice. But we are, in our lesser way, offerers too. Twice we are told so in the Ordinary of the Mass. We have already seen how after the Consecration the priest says, "We thy servants but also thy holy people [plebs tua sancta] . . . offer . . . a pure, holy and immaculate Victim." To see ourselves merely as spectators at Mass is to miss the opportunity to take our part in the highest action done upon earth.
One element in the Mass remains to be mentioned. We, united with Christ's priests, have offered Our Lord to God. And God gives him back to us, to be the Life of our life. That is what Holy Communion means. God, while retaining Christ for his own, also shares him with us. So that God and man, each in his own way, receive the slain and risen God-man.