The Three (or the Kindly Ones, as they prefer to be called) are a triad of goddesses consisting of the Maiden, the Mother, and the Crone. They are based upon the triple goddess myth, a tripartite deity that fulfills various functions. They can take many different forms, and often change positions among each other, but they always represent the same entity.
Among their divine aspects are the Fates (Moirae) and the Weird Sisters, and the Erinyes (Furies) are their vengeful aspect. As Furies, they persecuted oath-breakers, patricides, matricides, and other violators of divine law. Their relentless pursuit manifested in several ways, one of the most severe being the inducing of tormenting, self-destructive madness.
Around the time Lyta Hall conceived her child with Dream, the Furies identified Dream as a target of coming filicide; because they might take action against Dream due to the boon of death he granted to his own son, and because Lyta Hall was related to them, and suffered a nervous breakdown after the abduction of her son, the Furies offered her vengeance on Morpheus if she agreed to be their instrument of destruction. Lyta agreed, and the destruction of the Dreaming began. Mervyn Pumpkinhead was one of the few who actively took up arms to fight the Furies in The Kindly Ones and was destroyed. Fiddler's Green was killed by The Three in The Kindly Ones. Abel, too, was murdered by the Furies.
The Furies' attack on the Dreaming was so severe, that Morpheus was left with only one option in order to save his realm; his own destruction. The death of the incumbent aspect of Morpheus of necessity created a new Dream and the new incarnation manifested in Daniel Hall.
It is worth noting that during his journey to the Underworld, Orpheus made the Furies cry by playing his lute in order to gain an audience with Hades and Persephone. They claimed to have hated him for that.
The Furies later appeared in The Sandman Presents: The Furies published in 2002.