HE story here is simple. Paul was a prisoner in Rome. In that prison he met a young man named Onesimus (vs. 9-10). Onesimus happened to be a runaway slave. His former master was the man to whom this letter was addressed. Onesimus' master was Philemon. It is apparent from the text that Paul witnessed to and won Onesimus to Christ while they were in prison together. And, by God's grace, Paul and Philemon were already friends. So, although Onesimus became a positive and willing companion to Paul while in prison with him, after his release Paul sent him back to his master. However, this letter (sent in Onesimus' hand) was a passionate request from Paul that Philemon would refrain from punishing Onesimus for his dereliction. And above that, Paul called on his friend Philemon to treat Onesimus with every kindness, as if Onesimus were really Paul himself. And, the key word here is the word "receive" (vs. 12 & 17). Paul wanted Onesimus to be received.
Now, how could Philemon receive Onesimus? How could he readily & generously accept Onesimus without also forgiving him. The forgiveness that Paul expected from Philemon is apparent in the context. And it is important to note the foundation upon which this forgiveness & acceptance was to be offered. It was all for love. Paul testified confidently about Philemon's love for Christ, for the saints, & for Paul in particular. Paul expected Philemon to include Onesimus under his umbrella of kindness (vs. 9 & 16) – especially since Onesimus had professed faith in Christ (Galatians 6:10). Onesimus was no longer just a slave. He was a Christian brother.