From the LCMS website:

Philemon was a prominent first-century Christian who owned a slave named Onesimus. Although the name “Onesimus” means “useful,” Onesimus proved himself “useless” when he ran away from his master and perhaps even stole from him (Philemon 18). Somehow Onesimus came into contact with the apostle Paul while the latter was in prison (possibly in Rome), and through Paul’s proclamation of the Gospel he became a Christian. After confessing to the apostle that he was a runaway slave, he was directed by Paul to return to his master and become “useful” again. In order to help pave the way for Onesimus’ peaceful return home, Paul sent him on his way with a letter addressed to Philemon, a letter in which he urged Philemon to forgive his slave for having run away and “to receive him as you would receive me” (v. 17), “no longer as a slave, but as a beloved brother” (v. 16). The letter was eventually included by the church as one of the books of the New Testament.