Romans 16:3-5 meaning

Prisca (or Priscilla) and Aquila are notable members of early Christianity, a Jewish married couple whom Paul first met in Corinth (Acts 18:1). They accompanied Paul to Ephesus, where he left them (Acts 18:19). While in Ephesus, Prisca and Aquila met Apollos, a man who was passionate about preaching the Scriptures but only knew a little bit about what God had accomplished. Prisca and Aquila brought Apollos into their home and taught him more about God (Acts 18:24-26). 

Eventually, Apollos was commissioned by the believers in Ephesus to sail to Achaia (southern Greece, including Corinth), where he helped the Christians there and skillfully proved to dissenting Jews that Jesus was the Christ through the scriptures. Prisca and Aquila are fine examples of obedient, faithful believers who ministered well alongside and apart from Paul. When Christians live in faithful obedience, they have an impact on one another's lives. The gospel is spread, believers are discipled, and needs are met.

Paul asks that they greet Prisca and Aquila, my fellow workers in Christ Jesus, who for my life risked their own necks, to whom not only do I give thanks, but also all the churches of the Gentiles (vv 3-4). Paul refers to a time when Prisca and Aquila risked their lives for him; Paul thanks them not only from himself personally but on behalf of all the Gentile churches, which is quite an acknowledgment. 

Both Jewish, Prisca and Aquila's ministry was incredibly impactful on the Gentiles. Paul says to also greet the church that is in their house (v 5), implying that they have moved back to Rome, where they were originally from, and have started a church in their house. In his first letter to the Corinthians, Paul writes that Prisca and Aquila send greetings to the church in Corinth, since they were with Paul at the time (1 Corinthians 16:19), showing their partnership with Paul's ministry. In his second letter to Timothy, Paul also writes a greeting to them (2 Timothy 4:19).

Given that the overriding purpose of this letter is to empower the Roman believers to resist the teaching of false competing "authorities," mentioning prominent church leaders with whom he has personal experience would be a persuasive move. It would also not be surprising if Prisca and Aquila sent word to Paul of the slander being spread about his gospel in Rome. 

We can infer that Paul here is endowing his apostolic legitimacy upon Prisca and Aquila, his ministry partners. They had fled Rome due to persecution and met Paul in Corinth (Acts 18:2).They had ministered together for a time, and they risked their own necks for Paul's sake. We can deduce that Prisca and Aquila were faithfully teaching the gospel of grace in Rome, as they had learned it from Paul, and began to encounter severe opposition from the competing Jewish "authorities." 

It would seem reasonable to further deduce that they dispatched Phoebe to travel to Paul and inform him of their conflict and ask for Paul's aid, which he provided by writing this letter. Phoebe likely delivered the letter to Rome. Here at the letter's end, Paul provides a full endorsement of Prisca and Aquila, recommending them as leaders the Romans ought to follow. 

This hearty endorsement of Prisca and Aquila is in stark contrast to the condemnation Paul gave to the competing Jewish "authorities," saying "For the name of God is blasphemed among the Gentiles because of you" (Romans 2:24). In Chapter 2, Paul cited the hypocrisy of the competing Jewish "authorities," arguing that they routinely violated the very laws which they pressured the Gentile believers to submit to. 

Paul says to greet Epaenetus, my beloved, who is the first convert to Christ from Asia (v 5) on Paul's third missionary journey (Acts 19:10). As one of the first Gentiles to believe under Paul's ministry, Epaenetus would be a tangible reminder of Paul's mission and authority in the gospel. Again, since this letter is a defense of Paul's authority as an apostle and the gospel message he received from Christ, this mention would also add persuasion.

Though Paul's ministry is the most famous in the early church of the New Testament, there were many Christians who helped him every step of the way, living as believers ought to, serving one another.