for sin indeed was in the world before the law was given, but sin is not counted where there is no law. (ESV)
Men throughout all ages of time have wanted to excuse their sinful behavior. It would be conceivable for us to think that during the time before God gave the Law to Moses men did not sin. After all, how could they violate a law that they did not even know? The reality is men have sinned from Adam until now.
Paul is telling us here that sin was in the world even before the Law was given. A great way to understand this is to consider that most people believe that killing another person is murder. It is generally perceived, by Christians and non-Christians alike, that murder is wrong behavior. Most would even agree to the word "sinful."
How is it that even atheists can have some kind of moral code? How is it that non-believers can believe in such a thing as sin? They certainly are not in agreement with God's Law as given by Moses. Imprinted on our hearts is enough of a moral code that informs our conscience of right and wrong.
Sin was in the world before the Law was given. Sin is still in the world. When the Law came the consequences of sin became more clear. God has always punished sin. God has always held man to account for his actions. There is not one sin committed by a person that is ignored by God. Not now. Not ever.
Understanding the weight of all of our sin ought to encourage us to confess our sin to God and receive his free gift of forgiveness through Jesus Christ.