"She began by making the two sons of Atreus quarrel"

The two sons of Atreus referred to here are the Greek leaders and brothers Agamemnon and Menelaus. It was Menelaus’ wife, Helen, whom Paris took to Troy, beginning the war. Menelaus was king of Sparta, and Agamemnon of Argos (or Mycenae, depending on different traditions). Both were very powerful men amongst the Greeks.