Erinyes
The Erinyes (or "The Furies") were a trinity of lesser goddesses in Greco-Roman mythology, Alecto, Megarea, and Tisiphone, who governed Vengeance & Retribution and who were empowered to punish the wicked, especially oathbreakers. In Dungeons & Dragons, they were split up into two different monsters; the Erinyes of Planescape and the Furies of Ravenloft.
Planescape
Whilst technically preceding Planescape - the D&D Erinyes goes all the way back to the original 1977 Monster Manual - the "true" Erinyes of D&D was made most prominent when that setting was released for Advanced Dungeons & Dragons.
Traditionally, the Erinyes takes the name of its Greco-Roman origins and has absolutely nothing to do with the story. They're basically the Devil equivalent of the Succubus, being attractive fiends who resemble fallen - but still gorgeous - angels. Different attitudes to account for the different between Baatezu and Tanar'ri, but still the same basic concept.
The exception is in 4th edition, where succubi switched sides to the devils; now, Erinyes (given a more bestial makeover) were wrathful champions of hell, and essentially diabolic amazons.
Ravenloft
The Furies of Ravenloft are far more faithful to the actual mythology, consisting of three fiend-like entities who resemble harpies. But, as Ravenloft is the biggest Fuck YOu Players setting in D&D, they are twisted around in one key detail: whereas the mythological Furies punished the wicked, these furies are blights upon the goodly, as their charge is to prevent any evil soul in Ravenloft from trying to seek redemption. As in, they will publically rip you to pieces if you refuse to continue being an evil asshole.