What was the systematic murder by the nazis of jews and others called?

The correct answer is: "Holocaust".

The Holocaust was the systematic murder commited by the German nazi party against the Jews and other human groups that they considered inferior to the 'supreme Aryan race', such as gypsies from Eastern Europe, homosexuals, disabled people, communists and Spanish republicans, etc.   These groups had to be removed to prevent the contamination of the Aryans, according to the nazi ideology. This is why they deported members of the abovementioned human groups to concentration camps were they died undertaking hard labor duties or to extermination camps were they were massively killed in gas chambers.