Justification
Can we conceive of a greater question than, "How can a person be right with God?" Ever since man has existed he has tried to reach God on his own terms. But, sad to say, all of these efforts have failed and will continue to fall short of what God expects.
the need of man
Because of sin, man falls short of the glory of God (Rom. 3:23). As such, he is in need of deliverance from the guilt of his condition. Man's own conscience testifies to himself that he is in dire need of deliverance (Rom. 2:15), something the Bible calls salvation.
Unfortunately, man attempts to reach heaven through illegitimate means (Rom. 4:4) such as his good works, an affiliation with a religion, or through attempts to appease God through religious ceremonies. But none of that avails him a thing simply because God expects and requires perfection.
biblical justification
Man truly needs to be righteous, but not a righteousness of his own. In the gospel (or "good news"), "the righteousness of God is revealed" (Rom. 1:17), allowing God to justify man (Gal. 3:8). In justification, God pardons us on account of Christ's work, and declares us innocent and righteous.
This declaration is completely objective, or a declaration from God because He imputes our sin to Christ and imputes Christ's perfect obedience to us. This act is the grounds of our salvation and justification.
"And to the one who does not work but believes in him who justifies the ungodly, his faith is counted as righteousness" (Rom. 4:5).
"To him all the prophets bear witness that everyone who believes in him receives forgiveness of sins through his name" (Acts 10:43).
"just as David also speaks of the blessing of the one to whom God counts righteousness apart from works: 'Blessed are those whose lawless deeds are forgiven, and whose sins are covered'..." (Rom. 4:6-7).
"Therefore, since we have been justified by faith, we have peace with God through our Lord Jesus Christ...For as by the one man's disobedience the many were made sinners, so by the one man's obedience the many will be made righteous" (Rom. 5:1, 19).
"For our sake he made him to be sin who knew no sin, so that in him we might become the righteousness of God" (2 Cor. 5:21).
"Who shall bring any charge against God's elect? It is God who justifies" (Rom: 8:33).
"And such were some of you. But you were washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and by the Spirit of our God" (1 Cor. 6:11).
Once justified, sinful man in God's eyes has kept God's holy law perfectly. God declares him righteous and not subject to the penalty for sin, which is eternal damnation. Indeed, he is "justified" from all things (Acts. 13:38-39).
summary of justification
Even though God pardons sinful man, He remains just because He did punish sin (Christ took our punishment for us), yet also demonstrated mercy by pardoning and accepting sinners. The believer in Christ trusts in Christ alone for salvation (Phil. 3:8-9). So we are not saved by good works (Titus 3:5), but we do strive to live godly lives and perform good works because we are grateful to God for His salvation (2 Cor. 5:15).