What does Romans 6:18 mean?

Paul is thanking God for the change that has taken place in the lives of the Christians in Rome, to whom he is writing. They were once slaves to their sinful desires, as we all once were. Now, though, they have become obedient from their hearts and committed to obey the teaching of God's truth. In fact, Paul now writes, they have become the slaves of righteousness.

By this, Paul means that the Roman Christians are presenting themselves—their bodies and minds—to God to be used to accomplish His righteous purposes. It sounds odd to the modern mind, that Paul would describe this commitment to be used by God for righteous purposes as "slavery." And yet, Paul began this letter by describing himself as a "slave" of Christ, using the Greek word doulos: a bond-servant. His terminology in this verse uses the same root word. Still, Paul seems to say in the following verses that even this version of "slavery" is not the best concept to describe this commitment to serve God's righteousness. Instead, he uses this "human term" because of our limited ability to fully understand this change in our allegiance.