First things first. What's a "libation" anyway? If you've ever seen a movie or TV show where a gangster pours out liquor on the ground in memory of dead friends and family, then you have seen a libation in action. That's because, for the ancient Greeks and Romans, a libation was a ritual offering of some liquid – typically water, wine, honey, milk, or oil. There were many occasions when such offerings were made: before dinner, when making a sacrifice, when praying, etc. But one of the most important functions of libations – just as in the modern example of the gangster – was as offerings to the spirits of the dead.
Libation Bearers earns its title in the opening scene, in which Orestes and then Electra and her attendant women make ritual offerings at the tomb of Agamemnon (technically only Electra and the women make libations; Orestes offers a lock of his hair). Once you start to think about it though, you realize that, in a metaphorical way, the idea of bearing libations actually runs through the whole play. That's because the whole play, which its theme of revenge, has to do with what the living owe the dead. The act of offering libations is a concrete image for this overriding theme.