Romans 16:6-8 meaning

Paul asks that the Gentile believers greet Mary, who has worked hard for you (v 6). It is not clear what Mary did besides having worked hard for the Romans believers. Some Greek manuscripts recorded this name as Mariam, the Hebrew form of Mary, which would indicate that this woman was Jewish.

We read in Romans 12:10-13:

"Be devoted to one another in brotherly love; give preference to one another in honor; not lagging behind in diligence, fervent in spirit, serving the Lord; rejoicing in hope, persevering in tribulation, devoted to prayer, contributing to the needs of the saints, practicing hospitality."

Christians who are living as God desires will help each other and toil for one another. Serving each other and meeting needs is not always easy and could often be described as hard work.

Paul sends greetings to Andronicus and Junias, my kinsmen and my fellow prisoners, who are outstanding among the apostles, who also were in Christ before me (v 7). It is also not known who Andronicus and Junias were. They could have been husband and wife, as Junias can be masculine or feminine. My kinsmen is likely a term that means they are the same nationality (Jewish) rather than a reference to being biologically related. 

This would indicate that although the Roman church was predominantly Gentile, there were some Jewish members. It would be very helpful to Paul's defense against the competing Jewish "authorities" seeking to overturn the gospel of grace, to have some Jewish believers who take his side. Although we do not know much about the listed people in this chapter, it seems likely that these would have been the key leaders who would take up the fight and contend for the gospel of grace. It is inferred that these are the allies of Prisca and Aquila in their vigorous defense of the gospel of grace. 

Had there not been allies who took Paul's side, it seems unlikely Paul's letter to the Romans would have survived. We can infer that Paul's allies gained the upper hand, in that Rome became a vibrant center for the growth of Christianity. Some believe that, since the Roman Christians were willing to gladly die for their faith, this was the cause of the emperor moving his primary capital to Constantinople. 

It is not known where or when Andronicus and Junias were in prison with Paul, but he and all the apostles evidently thought very highly of them. When Paul says they were in Christ before me, he means that they became believers before him. Paul says to greet Ampliatus, my beloved in the Lord (v 8). We also do not know much about Ampliatus, but Paul called him his beloved in the Lord which shows Paul's love and admiration for him.