"Furies" is the Roman name for these three Greek goddesses, originally called the Erinyes or "angry ones." They were the children of Gaia, the original earth-mother, and her consort Uranus. Their task was to wreak vengeance on mortals who had wrongly committed murder. The best-known story involving the furies is told in Aeschylus' trilogy of plays about the House of Atreus. Orestes, son of Agamemnon, kills his mother in revenge for her murder of his father (itself in revenge, because Agamemnon had killed their daughter.) The Furies pursue Orestes until, eventually, the goddess Athene intervenes. It is formally decided that Orestes acted rightly in killing his mother (and her lover, who also hated Agamemnon's family) since a son's duty is to avenge his father. On the other hand a mother had no rights over her child, so her killing of Agamamnon could only be regarded as murder The Furies accepted this ruling and their name was then changed to "Eumenides" or kindly ones.
They were called they kindly ones because they spared Orestes. What Orestes did was not a crime but a rightly deed/