In Protestant, God forgiving our sins means our sin is covered by the blood of Christ. He no longer see our sins. He no longer show angry toward us. He no longer want to punish our wickedness and kill us anymore. He starts to love us again.
What does 'God's forgiveness' mean in orthodox church?
The best way to understand forgiveness is to read the Parable of the Prodigal Son.http://www.biblegateway.com/passage/?search=Luke%2015:11-32&version=NKJV
The father never hated the son. He always wanted the son to return. All it took for the father to forgive the son and take the son back, was for the son to return from his life of sin. So all it takes for God to forgive is repentance.
Orthodoxy does not see sin and forgiveness in legal / transactional terms. The way you have explained sin looks like the following scenario.
1) I parked at the wrong spot.
2) So the authorities are angry at me for not obeying their rules
3) So they want me to pay a fine.
4) For me to reconcile with the authorities, I have to pay the fine.
5) I am so poor, I have no money to pay the fine.
6) So a very loving man steps in for me and pays the fine for me.
7) Now that the fine is paid, I am free.
Orthodoxy does not view God as the city authority mentioned above; but as a loving father.
‘God chastises with love, not for the sake of revenge - far be it! - but seeking to make whole His image. And He does not harbour wrath until a time when correction is no longer possible, for He does not seek vengeance for Himself. This is the aim of love. Love’s chastisement is for correction, but it does not aim at retribution... The man who chooses to consider God as avenger, presuming that in this manner he bears witness to His justice, the same accuses Him as being bereft of goodness. Far be it, that vengeance could ever be found in that Fountain of love and Ocean brimming with goodness!’ St. Isaac the Syrian
I sure you are thinking; if this is the case, then what is the relevance of the 'cross'?. In orthodoxy we dont just look at the crucification alone. The focus is on the Resurrection of Christ and his victory over death.
Think of the fallen nature of men, as a disease (or corruption) that affected us. The whole purpose of the Incarnation, Earthly Mission, Crucification and the Resurrection of Christ, who took on our own form was to heal us from the disease and restore us from the corruption. St. Athanasius summarizes it for us:
God became man that men might be made gods.