This should get you started. From the Catechism of the Catholic Church:
**Christ’s death is the unique and definitive sacrifice **
**613 ** Christ’s death is both the Paschal sacrifice that accomplishes the definitive redemption of men, through “the Lamb of God, who takes away the sin of the world”,439 and the sacrifice of the New Covenant, which *restores man to communion with God by reconciling him to God * through the “blood of the covenant, which was poured out for many for the forgiveness of sins”.440
614 This sacrifice of Christ is unique; it completes and surpasses all other sacrifices.441 First, it is a gift from God the Father himself, for the Father handed his Son over to sinners in order to reconcile us with himself. At the same time it is the offering of the Son of God made man, who in freedom and love offered his life to his Father through the Holy Spirit in reparation for our disobedience.442
**Jesus substitutes his obedience for our disobedience **
615 "For as by one man’s disobedience many were made sinners, so by one man’s obedience many will be made righteous."443 By his obedience unto death, Jesus accomplished the substitution of the suffering Servant, who “makes himself an offering for sin”, when “he bore the sin of many”, and who “shall make many to be accounted righteous”, for “he shall bear their iniquities”.444 Jesus atoned for our faults and made satisfaction for our sins to the Father.445
**Jesus consummates his sacrifice on the cross **
616 It is love "to the end"446 that confers on Christ’s sacrifice its value as redemption and reparation, as atonement and satisfaction. He knew and loved us all when he offered his life.447 Now "the love of Christ controls us, because we are convinced that one has died for all; therefore all have died."448 No man, not even the holiest, was ever able to take on himself the sins of all men and offer himself as a sacrifice for all. The existence in Christ of the divine person of the Son, who at once surpasses and embraces all human persons, and constitutes himself as the Head of all mankind, makes possible his redemptive sacrifice for all.
**617 ** The Council of Trent emphasizes the unique character of Christ’s sacrifice as "the source of eternal salvation"449 and teaches that "his most holy Passion on the wood of the cross merited justification for us."450 And the Church venerates his cross as she sings: "Hail, O Cross, our only hope."451
439 Jn 1:29; cf. 8:34-36; 1 Cor 5:7; 1 Pet 1:19.
440 Mt 26:28; cf. Ex 24:8; Lev 16:15-16; 1 Cor 11:25.
441 Cf. Heb 10:10.
442 Cf. Jn 10:17-18; 15:13; Heb 9:14; 1 Jn 4:10.
443 Rom 5:19.
444 Isa 53:10-12.
445 Cf. Council of Trent (1547): DS 1529.
446 Jn 13:1.
447 Cf. Gal 2:20; Eph 5:2, 25.
448 2 Cor 5:14.
449 Heb 5:9.
450 Council of Trent: DS 1529.
451 LH, Lent, Holy Week, Evening Prayer, Hymn Vexilla regis.
I recommend you read this entire section in the Catechism. I also recommend Robert Sungenis’ book, How Can I Get To Heaven?