Paul talked about how even though God gives grace, that doesn't mean it's a good idea to sin. Then Paul talks a bit more about the significance of the law (for the Judeans who are very familiar with it). In particular, the apostle writes that "the law has dominion over a man as long as he lives" (7:1). This is basically the point of pretty much every legal system (especially since dead people can’t break laws).
One example Paul brought up is a marriage case where a woman marries a man but later marries someone else after her husband died (7:2-3). Intercourse with others shouldn’t be done while currently married, but even though the woman technically had more than one husband, pretty much no one considers this to be polygamy. Paul even talked about how "she is no adulteress" in that scenario (7:3).
Remember the part about being baptized to Christ's death back in Romans 6? Paul will explain even more significance of that in the following verses.