What does Romans 13:3 mean?

Paul has described the Christian doctrine of submission to human authorities. Since every human leader is established by God, Christians must not resist God's work by resisting those authorities. These verses give important context for understanding his recent comments.

Paul begins to describe why God establishes human authorities in the first place. The God-given role of governmental authorities is to keep order. This is true whether those authorities are good people or not. Broadly speaking, human government is one of the ways God restrains the influence of evil in the world (2 Thessalonians 2:7). Christians cannot embrace anarchy—rejection of all forms of government—or disobey authority simply because they disagree.

Paul describes the way to live without fear of someone in authority: Do good. Authorities are no threat to those who do what is right. In fact, they will approve of you. This teaching is certainly sound to the extent that those in authority are fair-minded and operate out of sense of integrity. Of course, our instinct is to recall moments in history where those in authority were most definitely a terror to people who were doing good, or at least not doing anything wrong, including Paul himself! The fact that Paul, personally, experienced ungodly government should give us pause before we dismiss his command as unrealistic.

Paul's point here is simply the general case. He's not interested—in this passage—in addressing exceptions. Paul's first concern is that Christians be known in their communities as people in submission to authority; those who do what is good. Believers ought not have a reputation as law-breakers living in needless conflict and rebellion against authority.

Of course, Jesus and nearly all the apostles, including Paul, were killed by those in authority over them, often for a refusal to obey laws that were in conflict with God's commands to them (Acts 5:27–29). This is a key subtlety in Paul's teaching: to "submit" does not necessarily mean to "obey." None of the apostles were killed for breaking laws merely for the sake of defying authority; they were "submissive" to the government when they refused to follow ungodly laws.