"Cognizable" means capable of being known or considered. It means capable of being judicially tried or examined before a designated tribunal.

A cognizable claim or controversy is one that meets the basic criteria of viability for being tried or adjudicated before a particular tribunal.

The term means that the claim or controversy is within the power or jurisdiction of a particular court to adjudicate.

In short: A cognizable crime is a crime that has been committed within the original jurisdiction of the court which is going to try the case.