I speak in human terms because of the weakness of your flesh. For just as you presented your members as slaves of uncleanness, and of lawlessness leading to more lawlessness, so now present your members as slaves of righteousness for holiness. (Romans 6:19)
The Roman Christians demonstrated that their baptism meant something to them by the way they lived.
They had lived a life of sin, but now they lived a life of service to God.
Paul’s illustration of slavery.
To help illustrate the spiritual principle of serving sin versus serving God, Paul has made several references to slavery in Romans 6. During this time of the Roman Empire, slavery was something everyone was all too familiar with.
He nearly apologized that he had spoken to them in terms found in daily life, such as slavery. In some ways, the raw language of slavery was probably distasteful to those at Rome, who may have experienced that cruel reality in their own lives. However, for Paul, it was necessary to make his point." - Pollard, Truth for Today Commentary, 218
The illustration of slavery and formerly serving a cruel master helped Paul make the point that Christians have been freed from sin to no longer serve that “master” again.
The difference in the Christian’s life.
Before they had been set free from sin by dying with Christ in the watery grave of baptism (Romans 6:3-7), they had “presented their members” as being “slaves” of what was unclean and impure. Their life of “lawlessness” led only to more and increased “lawlessness.” This reminds us of the Gentile’s downward spiral into sin in Romans 1:18-32.
Previously they had been the slaves of sin, and they lived lives of sin - and they were only diving deeper into that way of life.
But now, “having been set free from sin” (Romans 6:18), they served a new Master who called for a new way of living. Now they were called to live as “slaves of righteousness for holiness (or sanctification).”
Formerly their members had been used in worldly living; now they are to separate them from such worldly uses and dedicate them to the service of God. And that is sanctification. - Whiteside, Commentary on Romans, 141
Remember Paul’s point in this chapter: the gospel of Christ does not encourage sinful living.
The gospel of Christ teaches us that we have been set free from sin to serve a new Master and live a life dedicated to God. We now belong to God, and our lives should reflect that change.
Flee sexual immorality. Every sin that a man does is outside the body, but he who commits sexual immorality sins against his own body. Or do you not know that your body is the temple of the Holy Spirit who is in you, whom you have from God, and you are not your own? For you were bought at a price; therefore glorify God in your body and in your spirit, which are God's. (1 Corinthians 6:18-20)