What does Romans 13:6 mean?

Paul has been teaching the Christian doctrine of being submissive to our human authorities, including and especially government authorities. Christians are called to do this because we believe that God is the one who has put every human authority in their position. They exist to serve His purposes, including the purpose of punishing people who do bad things (2 Thessalonians 2:7). Context of this and other passages makes it clear that Christians are obligated to disobey government when—and only when—compelled to disobey God (Acts 5:27–29). As a general rule, believers are commanded to cooperate with their government authorities.

Now Paul gets to a specific example of submission to human government: paying taxes. Christians are taxpayers, Paul writes, because those taxes support the work God intends to do through the human authorities He has put in place. Even when those men or women stand against the truths of God, their fundamental role as order-keepers is still part of God's will.

This was a controversial position even among the Jewish leaders of Jesus' and Paul's day. Critics tried to trip Jesus up by asking Him if it was lawful to pay taxes to the Roman ruler, Caesar. Jesus, pointing out that Caesar's picture is on the money, stated flatly that the taxes should be paid (Matthew 22:15–22). In a similar manner, some in the modern day have suggested Christians should not pay taxes if the government is funding evil practices. Jesus and Paul disagree. Both paid taxes to the same government that ultimately killed them and persecuted other Christians, as well. Neither endorsed the option of not paying taxes as a matter of conscience.

Paul's larger point is that we must trust God to provide for us as His children. In the case of this passage, that includes provision through the government authorities He puts in place. God is fully capable of using them for our good no matter who they are or what their intentions.