The term now used to describe the nazis’ strategy to exterminate european jews and other groups is the

 The HOLOCAUST

Context/details:

The Holocaust is a term used to describe the systematic mass slaughter of European Jews and others in Nazi concentration camps during World War II.

Holocaust" is a term that means "burning the whole thing."  It comes from terms related to burnt offerings of animals in ancient religions. Essentially, the unwanted Jews and others in Germany were treated like animals to be slaughtered.  You can find appearances of the term "holocaust" in use already during World War II, such as the records of Britain's House of Lords in 1943 noting that a member there had asserted that "the Nazis go on killing" and urging some relaxing of immigration rules so that "some hundreds, and possibly a few thousands, might be enabled to escape from this holocaust.”  But the term gained its main currency as historians in the 1950s began to use the term in reference to the Nazi's campaign of genocide.

By the way, the term "genocide" is another that came into use around the same time.  Raphael Lemkin, a Polish legal scholar (of Jewish ethnicity) had been studying the problem of mass killings of a people group since the 1920s, in regard to Turkish slaughter of Armenians in 1915.  He coined the term "genocide" in 1944, in reference also to the Holocaust.  The term uses Greek language roots and means "killing of a race" of people.  Lemkin served as an advisor to Justice Robert Jackson, the lead prosecutor at the Nuremberg trials.  "Crimes against humanity" was the charge used at the Nuremberg trials, since no international legal definition of "genocide" had yet been accepted.  Ultimately, Lemkin was able to persuade the United Nations to accept the definition of genocide and codify it into international law.  

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