In the first three chapters, Paul talks about how all of us have done some not-so-good actions before and thus have a "sin" problem. It is a hard topic to talk about, but it is an important one nevertheless (after all, God wants to solve problems).
To summarize the section, Paul talks about the significance of the law. In particular, because of the law, "every mouth may be stopped" and "the world may become guilty before God" (3:19). In other words, because of the law (whether it is moral conscious or the Mosaic Law), we know that we screwed up.
Additionally, from these screw-ups, Paul states that "no flesh will be justified in His sight" (3:20). We can't use the law to show that we're good because the law shows that we have done some bad things before.
In summary, the law shows that we are guilty of at least one sin (very likely more than one). That's no good, and that's a big problem, but now what? The good news is that God provides a solution to the sin problem, and Paul will talk about it in the next few verses.