In the Reformed faith, justification is the one-time offering of Christ for His sheep. Christ suffered, died and was resurrected for our sins. Those sins, every last one of them, have been paid for by the shed blood of Christ.
We have been redeemed.
Justification means we are right in God's eyes because of the work of His perfect Son on our behalf. We could not save ourselves. Christ saved us. He took the punishment due us, thus enabling us to now stand acquitted before God.
Justification is a judicial act of God, in which He declares, on the basis of the righteousness of Jesus Christ, that all the claims of the law are satisfied with respect to the sinner -- (L. Berkhof, Systematic Theology, p. 513). "The phrase in ipso (in him) I have preferred to retain, rather than render it per ipsum (by him,) because it has in my opinion more expressiveness and force. For we are enriched in Christ, inasmuch as we are members of his body, and are engrafted into him: nay more, being made one with him, he makes us share with him in every thing that he has received from the Father." -- (John Calvin Commentary on 1 Cor 1:5) "This calling is an act of the grace of God in Christ by which he calls men dead in sin and lost in Adam through the preaching of the Gospel and the power of the Holy Spirit, to union with Christ and to salvation obtained in him." -- Francis Turretin"Those whom, God effectually calls he also freely justifies, not by infusing righteousness into them, but by pardoning their sins, and by accounting and accepting their persons as righteous; not for anything wrought in them or done by them, but for Christs sake alone; not by imputing faith itself, the act of believing, or any other evangelical obedience to them as their righteousness, but by imputing the obedience and satisfaction of Christ unto them, they receiving and resting on him and his righteousness by faith, which faith they have not of themselves, it is the gift of God" - Westminster Confessions of Faith, Ch. 11.
Something I learned was Catholics have reinterpreted the atonement as well. There is no mention of Christ dying as a subsitute for your sins. That's simply because they have reinterpreted the atonement to mean it was only an act of love.