Recently I’ve been thinking about what the whole bible really is telling us - the basic message it shows us about God (looking at the Bible as a whole, from a distance). The story of humanity is primarily of man in a state of sin and rebellion against God and His redemptive plan to bring us back to Himself. As Christians we focus on our salvation through Christ's sacrifice for us (as we should). However I think that sometimes we sort of gloss over the issue of sin because we know that Jesus has removed much of that burden from us. However, I think it is essential we understand the significance of sin, so we can grasp how perfect God is, our need for forgiveness, and the significance of Christ's sacrifice for us.
Part 1 - Sin
Jesus tells us that the greatest commandment is to have an attitude of love for God (Mark 12:30). A life pleasing to God is one that has moral purity not only in its actions, but also in its desires of heart. Aside from what is included in the 10 commandments (Exodus 20:17), the Bible shows us that less 'obvious'/ attitudinal things such as Anger (Matthew 5:22), Lust (Matthew 5:28) Jealousy and selfishness (Galatians 5:20) are considered sins. Wayne Grudem (Systematic Theology) defines sin as "any failure to conform to the moral law of God in act, attitude, or nature.” Sin covers a lot really.
This is probably why a huge chuck of the Bible is concerned with showing us that EVERYONE is sinful as we are unable to conform to the moral law of God in act, attitude, or nature (Few example: No one is righteous (Romans 3:9-30; 5:12-14); We are sinners by our very nature (Romans 5:8) and children or Wrath (Ephesians 2:3)). What the Bible shows us is that we are unable to live a life which is completely righteous and thus completely lacking of sin.
Significance
Matthew 25:46 tells us that God's justice is that the righteous will gain eternal life while the unrighteous will go to eternal punishment. As was just explained, noone is righteous - which causes a bit of an issue for us all really. We NEED saving. Without a way to be forgiven by God (which we do not deserve, it is purely from His mercy), things are looking a tad grim.
Part 2 - Grace (the good news)
God knows that we can't live a fully righteous life, thus we require forgiveness. It would be unjust for sin's not to be punished, therefore He took it upon Himself for justice to be achieved (John 3:16) - this is the idea of Propitiation: Christ has removed us from the wrath of God which we deserve (1 John 4:10). He has redeemed us back to God (Romans 3:23-24). He has made it so we are cleansed from all unrighteousness (thus can have eternal life) when we confess our sins (1 John 1:9). Not only does he forgive us, Micah 7:19 says, "He will again have compassion on us, and will subdue our iniquities. You will cast all our sins into the depths of the sea." This is pretty cool - God has given us a way to have our unrighteousness paid for thus enabling us to have eternal life rather than punishment.
Glory of God
The beauty of our salvation through Gods actions, not our own, is that we cannot boast that we have somehow earned it, as Ephesians 2:8-9 "For by grace you are saved through faith, and this is not of yourselves, it is the gift of God; it is not of works, so that no one can boast." God has saved us through His works, not our own. All glory for our salvation can only be given to God, as He has done everything. The system of sin therefore essentially shows us that God is amazing, so much better than us, so magnificent, that even our most valiant efforts to live a righteous life is unable to compare to Him. Yet he is so rich in compassion, mercy, and love for us that he has taken the initiative and saved us through His actions. The majesty of God is so hard to even comprehend and it is only increased when you think about the significance of sin and His actions to save us from what we deserve.