Upon his return from the Trojan War, Agamemnon, king of Mycenae, is killed by his wife Clytemnestra and her lover Aigisthos. Their daughter Elektra sends her brother Orestes into exile to protect him. According to the version told by Aeschylus in the Choephoroi, the second play of his Oresteia trilogy, many years later Clytemnestra is troubled by dreams and so sends Elektra to the tomb of her father to pour libations. There she meets her brother who had come with his friend Pylades to dedicate a lock of hair. Once the siblings are reunited, they decide on vengeance for their father's death, which Apollo has ordered Orestes to carry out.
It is this recognition scene from the Cheophoroi that inspired many South Italian vase-painters. For an example from Paestum by the Boston Orestes Painter and a list of other versions see no. 105 in Padgett, et al., Vase-painting in Italy, Red-figure and Related Works in the Museum of Fine Arts, Boston, and no. 112 in Mayo, The Art of South Italy, Vases from Magna Graecia. For a hydria by Python depicting the recognition scene which includes Pylades but not the Fury, see no. 250 in Trendall, The Red-figured Vases of Paestum.