Double criminality (also known as dual criminality) is a crime punished in both the country where a suspect is being held and a country asking for the suspect to be handed over or transferred to stand trial.
In other words, the crime in one country has to also be a crime in the country extraditing you. This principle is not universally used - notably, it is not recognized under the European Arrest Warrant system.
Double criminality is a requirement in extradition procedures from the United States of America as extradition is allowed only for offenses alleged as crimes in both jurisdictions.