Paul writes this letter as an older brother pleading on behalf of a younger brother to a brother for forgiveness. Paul asks Philemon to except Onesimus as he would Paul himself. Paul is surety for his brother; he tells Philemon that if Onesimus owes him anything charge it to my account. He makes mention to Philemon that he owes him his own life as well.
The is the picture, God has forgiven us and we owe Him our very lives. If someone comes to you for forgiveness no matter how badly they have hurt you they are to be forgiven. Truly forgive as God has forgiven us in Jesus Christ.
For the Bible text use this link: http://olivetree.com/read/nasb/Philemon/1