In order to understand this quotation, you need to understand the back story of the Trojan war. Artemis punished Agamemnon for an act of transgression. He killed a deer in a sacred grove. As a punishment, as Agamemnon was about to sail for Troy, there was no wind. Calchas, a seer, stated that the only way to appease the goddess was to sacrifice his daughter, Iphigenia. So, he did the unthinkable.
This action, of course, made Iphigenia's mother, Clytemnestra, furious. So, when Agamemnon came back from the Trojan war, Clytemnestra was plotting his death. In a bath, Clytemnestra gets her revenge.
In light of this, the words of which you speak, are spoken at the beginning of the tragedy to show what will happen. Agamemnon will be killed. A killer will be killed. In a word, there will be justice.