Einsatzgruppen were Nazi mobile killing units that followed the German army into the Soviet Union after Barbarossa started in 1941. They rounded up Jews, Roma, communists, officials, and other civilians, then carried out mass shootings, often with help from police battalions, Waffen-SS, and local collaborators.
They were basically organized mass murder squads, chief. Places like Babi Yar are infamous examples. If you want, I can explain how they coordinated with the army/admin side in normal-human terms.