Character Analysis
For more info on Clytemnestra before she got ghostified (that is, er, killed by her son Orestes), check out the other two plays of the Oresteia trilogy (Agamemnon and Libation Bearers).
In The Eumenides, the Ghost of Clytemnestra plays a pretty simple role. After Apollo has sent Orestes on his way to Athens, the Ghost shows up and wakens the Furies to head after him. In this way, the Ghost of Clytemnestra represents the anger of the victim of a crime that demands the satisfaction of vengeance.
(Clytemnestra): "[…] I was slaughtered by the hands of a matricide. See these blows, see them with your heart!—the mind asleep is given clear light by the eyes. You licked up many enough things from me, libations without wine, plain offerings of appeasement. […]" (94-116)
Yeah. She's steamed. She's so mad, in fact, that she starts getting belligerent to the Furies about not punishing her son thoroughly enough. But in her rant she lets a crucial detail slip. Those "libations" and "plain offerings of appeasement" make it clear that Cly was pretty sure that she was going to get done in… so sure, in fact, that she started making the revenge-happy Furies sacrifices in advance.
So basically she set up an insurance policy for her afterlife: she made sure that her son would get paid out (in being made miserable) by the Furies. Pretty clever, if we do say so ourselves.