A legal word, extradition means sending someone back to the country or state where they've been accused of a crime. Getting countries to agree on the terms of extradition can take years.
It can be hard enough for lawyers in the U.S. to agree on a person's extradition from one state to another, so you can imagine how difficult it can be for officials from different countries. Extradition can have real consequences for the person being extradited. Suppose the laws there allow for the death penalty: a person accused of a capital crime would be smart to fight extradition to that place. The Latin prefix ex- means "from, out of," and trāditiōn- means "handing over," so extradition is the handing-over of someone from one jurisdiction to another.