Ancient letter-writers typically ended their messages with some greetings to the recipient of the letter and others who lived in the same city and were friends or colaborers with that person. Since Romans 16 represents the conclusion of Paul's epistle to the church in Rome, we find in the chapter his greetings to specific Christians who lived there.
The Apostle first mentions a woman named Phoebe, and he does so by way of commendation and not a greeting. He does so because Phoebe was not a resident of Rome but rather lived in the city of Cenchreae. The Apostle calls her a "servant," and he uses the term diakonos, which is the same word translated elsewhere as "deacon." This is one reason many Christians believe that although women are not to be ordained to the office of elder (1 Tim. 3:1-7), they may be ordained to the office of deaconness and perform the duties of a deacon, particularly in serving women in the congregation. Other believers disagree, and they do so based on texts such as 1 Timothy 3:8-13, which talks about deacons' wives and implies that they will help their husbands minister to women in the church, but does not give them the title of deacon or deaconness. The debate continues among good and godly people, and we do not have space to go into it in detail here. We will just note Dr. R.C. Sproul's comments on the matter in his commentary Romans, where he says that even if the passage does not endorse the ordination of women as deacons, it does point out the importance of women serving in the church. From day one, women have exercised their gifts as members of the body of Christ, and they, no less than men, should be encouraged and allowed to serve wherever it is appropriate.
Phoebe was a dedicated servant of the first-century church, which we see not only in Paul's calling her a "servant" but also in the fact that she was most likely the person who brought his epistle to the Romans. This Apostolic commendation indicates that the Roman Christians likely did not know Phoebe, and so the believers would need a good word from Paul about her in order to welcome her as a friend and sister. They were to welcome her in a manner "worthy of the saints" (Rom. 16:1-2). In other words, they were to show hospitality and give her food, lodging, and whatever else she might need during her stay in Rome. She was a sister, and because she had supported Paul's material needs in some way (she was his "patron"), they were to receive her in the Lord.
When others serve faithfully, it is appropriate to recognize them for what they have done. In the case of Phoebe, this meant that it was right for the church at Rome to receive her with open arms and to provide for her needs. In our day, this means showing hospitality to our brothers and sisters in Christ—especially if they have served faithfully. We might also recognize and encourage a brother or sister for a job well done in a more public way, if it’s appropriate.