This is a great play, even though it is very difficult to translate from the Greek. This is the hardest play that I have ever translated. With that said, here are few points.
First, you need to understand a bit about the context. Agamemnon was the leader of the expedition to Troy. However, as he was leaving, there was a problem, as he offended the gods. To atone for his transgression, he has to offer his daughter, Iphigenia, to gain favorable winds. Agamemnon, rather than calling off the expedition, he does the unthinkable.
Second, of course, his wife and the mother of Iphigenia, is outraged. So, while Agamemon is gone off to war, she plots to kill him. After ten long years, Agamemon returns and Clytemnestra welcomes him and there is no sense that he is going to kill him. She is masterful in hiding her intentions.
Third, we can see great hubris in the fact that she slays her husband, which is unthinkable (as well) in the bath. There is also a religious connotation, because it is a bath to purify himself. She, therefore, takes matters into her own hand a she meets the murder of her daughter with the murder of her son. This, then, in turn creates blood guilt that does not leave the family. The Orestia is the story of this blood guilt, which stated in hubris and has been sustained by it as well.