Saarinen gives two paragraphs that I thought were helpful in his introduction to the letter. He writes:
The purpose of Philemon is obvious: it is a letter of recommendation that should accompany Onesimus and create good will in Philemon so that he would not punish the returning slave. On the way home, such a letter may also to some extent protect the fugitive slave from imprisonment by legal authorities. Other similar letters are known; the most famous is the letter of Pliny the Younger to Sabinianus from around AD 110. In this letter, quoted in many commentaries on Philemon... Pliny appeals for a freedman who has run away and thus violated his duty of servanthood. Like Paul (Phlm. 16), Pliny pleads for a relationship of brotherly love between the servant and his master and recommends the returning servant as worthy of such love.
Although Philemon was originally composed for this practical purpose, the epistle also creates a "symbolic universe"... in which a prisoner, Paul, pleads for the release or at least for the kind treatment of another nonfree person, Onesimus. Neither Paul nor Onesimus is free, but their being Christian transcends external boundaries. In a paradoxical manner, the epistle stresses joy, love and confidence between people in chains. Christians have become prisoners "of" and "in" Jesus Christ (Phlm 9, 23). Although Philemon is a practical and occasional piece of writing, it also contains a deeper message. In the exposition, this deeper message relates to freedom, love, and gratitude as the motivational grounds Christian behavior. It is further noteworthy that Philemon is addressed not only to Philemon but to the church (vv. 2, 25)