This is a letter written by Paul to a brother in Christ named Philemon. This is a letter about forgiveness. It seems that Philemon had a slave named Onesimus. The name Onesimus means useful, but it seems that Onesimus was not very useful. It also seems that Onesimus left Philemon and likely with some of his goods. Paul met Onesimus in his imprisonment, perhaps Onesimus was imprisoned as well for stealing or as a runaway slave. It seems while with Paul in his imprisonment Onesimus came to repentance and faith in Jesus Christ.
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