What does Romans 7:9 mean?

Paul describes himself as someone who once lived with no awareness of the law. In that state, he was "alive." He doesn't suggest by this that he was without sin. He seems to be speaking about his own awareness—his perspective. He was alive, in some sense, spiritually. At least, he had no awareness of his spiritual disconnection from God. This is a matter of perception—Paul saw himself in one way, only to find his perspective was wrong.

A few scholars suggest that Paul is describing mankind in general here, perhaps referring to the time before God gave the law to Moses and Israel. Most, however, disagree. When Paul, and people in general, learned about God's law, they died spiritually. That is, it was the law that made Paul aware of his own sinfulness and separation from God. The law showed Paul that he was a sinner and not a righteous person. This is not unlike a person who enters a doctor's office thinking they are "alive," but leaves with a diagnosis that death is imminent—all that really changed was their perspective.

This is why Paul insists that, in spite of the law being a good gift from God, it is not how God intends for us to become righteous people. The law is how God intends for us to learn that we are sinful people.