All the bloody acts of revenge that go down in Orestes and Electra's family are kind of an allegory for a whole way of living. Way back in the day, it was standard practice for you to take revenge for the death of someone, by killing the killer yourself.
Though this does still happen from time to time, we think it's safe to say that this practice is generally frowned upon. The rise of laws and courts has largely done away with blood feuds. (Well, in a lot of places anyway.) When Orestes is acquitted of his crime, ending the cycle of retribution, the verdict represents the way in which all society is moving toward less violent methods of conflict resolution.