For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin. (ESV)
I don't particularly like mirrors. They have a terrible way of exposing all of my imperfections. In fact, the better the mirror, the worse I look. It would be one thing if I had a magic mirror that had a way of actually removing the imperfections that it exposes, but sadly there is no such mirror. Mirrors point out flaws, but they do nothing to fix them.
Paul is talking about the Law. Through the law comes knowledge of sin. Imagine the Law of God as a spiritual mirror. The deeper you look into it the more evident it is that you are sinful. You are flawed. You have many imperfections. The Law perfectly exposes sin, but it does nothing whatsoever to get rid of the sin.
By works of the Law no human being will be made right with God. Why? We are not able to keep the Law the way the Law demands to be kept. The Law is God's righteous, perfect, holy standard. We do not even come close. Paul is making a very important point for us about the purpose of the Law. The Law is not intended to make us holy, it is intended to show us how unholy we are.
There were Jews in the Old Testament who thought they were keeping the Law. Jesus came and showed them that they not only were not keeping the Law, but the Law demanded even more than they had understood. In the Sermon on the Mount Jesus tells those who thought they were not adulterers that one lustful look was enough to convict them. Their murderous attitude was just as condemning as the act of killing another person.
Do you feel exposed? Imperfect? Flawed? Turn to Jesus Christ. He offers a way to make you perfect, holy, and right with God. He lived the Law for you, perfectly. Place your faith in his work on your behalf.