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

The term that we most commonly use today is the holocaust. This is the term that is being used to describe the horrific strategy of the Germany in WW2 which was infused with Nazism as an ideology. 

This included eradicating different ethnic groups such as gypsies, people of colour, jews, and enslave other ethnic groups (slavs for example).