What does Romans 13:8 mean?

Paul transitions here from discussing what is owed to human authorities, including respect and honor, to what is owed to everyone.

The command to owe no one anything should not necessarily be read as a command to Christians never to borrow money for any reason. The sense of the Greek is that we should not let any debt remain outstanding—that we should not keep on owing anyone for anything. That may be understood as a requirement to always pay what we owe in a timely manner according to whatever agreement we have made with the lender. Or, put another way, to not live lives of constant dependency, borrowing, or unreliability.

In truth, however, Paul is not primarily concerned with money here, as the following verses will show. He wants to talk about our obligation as Jesus-followers to love other people, including our neighbors. He seems to say that loving others is a debt we will never pay off. We will never be done with "paying" love to each other.

How does continuing to pay our debt to love others fulfill the law, exactly? Paul is reflecting what Jesus said are the two greatest commandments, to love God and our neighbors (Mark 12:29–31). Paul will show in the following verses that Christlike love will naturally motivate us to keep all the other relationship commands in the law.