Pardon my ignorance but what is the Einsatzgruppen?
Literally "Special Action Groups" they would follow the armies into conquered territory and were used for killing political opponents, communists, and Jews. They killed possibly 2 million of the 6 million Jews in the Holocaust by shooting in mass burial pits in Eastern Europe, and were frequently aided by locals. Even for ideological fanatics like these, the psychological toll was extreme of 24/7 killing. Himmler promoted the construction of death camps to humanely "spare" his men, and also increase effectiveness.
theFIRMboss's answer is better.
I believe the literal meaning is special group, but I don't speak German so I might be wrong on that. The Einsatzgruppen were part of the SS that were responsible for exterminating people, mostly in the areas that were newly conquered. As the death camps became established and the tide of battle turned they were phazed out.