The Epistle to Philemon is not strictly speaking a pastoral epistle, as it does not concern the pastoral care of a church. It is, however, a very personal letter written to Philemon, who was a leader in Colossae of some means and influence. Philemon had a slave by the name of Onesimus, who ran away to a major city, most likely Ephesus, where he became a Christian and met Paul.
Paul knows that Onesimus must return to Philemon, and so writes a letter to Philemon in order to plead for Onesimus’ favorable return. We know that a later bishop in the area was named Onesimus, so Paul’s letter appears to have been successful, and perhaps Onesimus included this letter in the canon of scripture to show a more personal aspect of Paul. Paul appeals to Philemon by reminding him of his reputation for love, and thus sets the stage for his plea to Philemon.