1. Pertaining to a location outside a country's boundaries: In the story, James was caught fishing in extraterritorial waters which did not belong to the kingdom where he lived and so he was not allowed to go fishing there again!
2. Of or relating to people who are exempt from the legal jurisdiction of the country in which they reside: An ambassador, or someone from the embassy of one country, has extraterritorial rights that are free of the legal authority of the nation in which he or she lives.