Double 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

European Arrest Warrant

The European Arrest Warrant is an arrest warrant valid throughout all member states of the European Union . Once issued by a member state, it requires the receiving member state to arrest and transfer a criminal suspect or sentenced person to the issuing state so that the person can be put on...

system.

In the USA

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.