Please read the
Catechism of the Catholic Church for a complete answer to this.
Here is an excellent selection from the Catechism about Christ’s death:
As you can see, Jesus’ suffering and death was prefigured in the Passover meal of Exodus and commemorated faithfully by the Jews. “On the tenth day of Nisan, take a lamb. It must be without blemish…” On the tenth day of Nisan, Jesus entered into the holy city of Jerusalem. Pontius Pilate declared at his trial, “I find no fault in this man.” Jesus celebrated the Passover with His disciples but that Passover was not complete until Jesus himself, the Paschal lamb, was slaughtered once and for all for forgiveness of all our sins.
There is a wealth of information in the Catechism; this in turn is drawn from Holy Scripture as well as the Tradition of the Church. My own knowledge about the Passover is due in considerable part to Jeff Cavins’ “The Great Adventure” Bible study course. I highly recommend it for a full understanding of how the Old and New Testament are finely interwoven, and how they represent a complete picture of our salvation as a people.
By His death, Christ abolished the Jewish temple worship based on sacrifice of animals. In creating a new covenant with us, He freed us from the bondage of sin once and for all. First comes our faith in His death and resurrection. Then come our good works based on our faith. As you know, Catholicism does not subscribe to the Protestant maxim of
‘sola fide’, faith alone. Our salvation is dependent on not merely the absence of sin, but on the presence of good works. This is first and foremost a participation in the sacramental life of the Church. Baptism, the Holy Eucharist, and Penance are all the keys to our salvation, as Christ instituted these while on Earth with His disciples. Do not forget acts of charity and love. In seeking forgiveness for our sins and frequent reception of the Eucharist, we perpetually recall Christ’s suffering, death and resurrection. This is what it means to live a life in Christ.