Now the law came in to increase the trespass, but where sin increased, grace abounded all the more, (ESV)
From the first sin in the Garden of Eden mankind was stained with a sinful nature. From Adam to Moses man lived in sin. By his very nature he did the things that were against God's holy nature. Even though there was no written code for them to live by mankind nonetheless lived in violation of God's standards.
When God gave the Law to Moses it made things worse for mankind. Paul says that the law came in to increase the trespass. This means that now that man had the written code of what God required it showed just how sinful man was. It is one thing to be in violation of law, but not know it. It is quite another to know what the Law says and walk in open rebellion to it.
Imagine riding your car on a highway in a place where you have never been. As you are enjoying a country ride you fail to see a posted change in the speed limit. A few minutes later you see the flashing blue lights in your mirror. You can tell the Police Officer that you did not know what the Law was, but you are still guilty of breaking it. If you had seen the sign you would be "more guilty."
What is the remedy? Where sin increased, grace abounded all the more! The Law shows us just how guilty we are. It is intended to help us to see our great need of a Savior. Some have referred to the Law as a tutor schooling us of our need for Christ. Spurgeon once said, "I have a great need of a Savior, and a great Savior for my need."
When it comes to breaking the Law of God we are all guilty. You can either choose to live in your open rebellion or you can choose the wonderful grace offered to you through Jesus Christ. You have a great need of a Savior, and a great Savior for your need.