Philemon is an interesting book in that, being one of the shortest in the Bible, contains only 430 words and twenty-five verses in the King James Translation. The main subjects of the book are Onesimus, a slave, and Philemon, his master and owner who is a Christian and friend of the Apostle Paul.
Onesimus, who likely lived in or near the city of Colosee (he delivered the letter to the Colossians to them), stole something from his master (Philemon 18 - 19) and then fled to Rome. While in the Roman capital he tracks down where Paul is in prison awaiting his trial.
After Onesimus hears the gospel, for an unknown period of time, he becomes a Christian. Paul, knowing of Onesimus' theft which he repenting of, decides the right thing to do is to send him back to his master with a personal note from him. He is hoping to convince his dear friend Philemon not only to forgive his slave but also to begin treating him with the same respect as a fellow believer.
The Apostle begins his direct appeal to Philemon by stating, "I beseech you for my son, Onesimus, whom I begot in my bonds" (verse 10). He then writes the following.
Who was once of no service to you, but now he is profitable both to you and to me; whom I am sending back to you (Philemon 1:11).
First century readers would have found Paul's play on words, using Onesimus' name, funny. Onesimus' name is translated from the Greek Onesimos, which means someone or something that is profitable or useful (Thayer's Greek Definitions).
The Apostle is stating that Onesimus was, at one time, not living up to his name when he was of "no service" to Philemon his master. Now, however, due to his conversion, he was finally fulfilling the destiny of his name by being of great use to both of them!