Simon the Pharisee had invited Jesus to dinner, but ignored the customary polite welcome (Luke 7:44-46).  Instead, an immoral woman who gate-crashed the party demonstrated grief over her sin and faith that Jesus would accept her (Luke 7:36-38).  Teaching Simon through a parable, Jesus explained that forgiveness was central to God’s heart and His mission (Luke 7:40-47).  The woman was forgiven because she openly admitted her sin, whereas the religious leader did not think he needed to be forgiven: his self-righteousness blinded him to the reality of his own sin.   

When Jesus announced that He had forgiven the woman’s sins, there was indignant muttering.  This was an outrageous claim because surely only God can forgive sins (Luke 5:20-26).  The answer should have been obvious: if Jesus forgives sins, He must be God!  Jesus knew that when He died on the cross, He would personally be paying for that woman's sins ... so He had every right to forgive.  Her peace came because He paid the price (1 Peter 3:18).

If somebody owes you money but cannot pay, you might choose to cancel (forgive) the debt.  But it would be wrong to think you can cancel a debt owed to somebody else; because the money belongs to the creditor and not you.  Every sin has to be paid for, but what is the price and who has the right to extract the price or to forgive?  The penalty for sin is death and eternal separation from God: therefore only God has the right to demand payment.  In the same way, only God can forgive (cancel the debt).  The amazing thing is that God's forgiveness comes at great cost to Himself (2 Corinthians 5:21).  See www.crosscheck.org.uk to know more.

The woman may not have understood all that, but she did believe that Jesus was her only hope.  She put her faith in Jesus to do something to help her, even if she did not know how.  It is the same today: all those who call on the Name of the Lord will be saved (Romans 10:13).  So, if you are despairing about yourself, go to Jesus trusting Him to do whatever is right for you.  If others do not know what to do - tell them to go to Jesus and trust that He knows what to do.  When it comes to sin and failure, He certainly knows how to forgive and has already paid the price to discharge the debt - so go to Him in faith and believe that His forgiveness is real, and for you personally.  Then you can go on your way in peace.