The term "common law" is one that is used more by the British than by Americans, which is one reason why the Framers of the Constitution used it even though it is not so familiar to us today. The common law is law that has been created by the precedents set in court cases. This is in contrast to law that has been set out by statutes passed by legislatures.
The basic idea behind common law is that the decisions made by courts in the past should determine what the law is today. This is the idea of stare decisis--the idea that precedents from past cases should be honored unless there is a very good reason not to. This idea is generally applied to torts and contracts, not to criminal law.
So, common law is law that is based on precedent from past court cases, not on law.