The great twentieth-century American novelist, William Faulkner, famously said about the American South that there the past is not only not dead, it isn't even past. That can help us understand the sacrifice of the mass as a re-presentation of Christ's sacrifice on Calvary.
The Catechism of the Catholic Church makes this clear:
The sacrificial memorial of Christ and of his Body, the 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
When we go to mass, we need to bear in mind that we are not simply remembering an event that occurred long ago. Not only is Jesus really present in the Eucharist, but his sacrifice on the cross is, in a mystical way, present as well. Jesus is not dead, and He is not a memory, but He is there, with us, and we with Him.