When Agamemnon comes home, he finds (too late) that Aegisthus and his wife Clytemnestra had been having an affair. Aegisthus invited him over for a feast, and then he killed Agamemnon and a bunch of his noble men. Clytemnestra killed Priam's daughter as well. She would not go near Agamemnon, and his wrath has been strong ever since that moment.
This is important because Agamemnon warns Odysseus to be wary of his wife upon his return. He is to make sure that she has been faithful all these years, or he may face the same demise. He tells all this to Odysseus in the Land of the Dead.