The poet Hesiod describes the Fates in his Theogony. According to Hesiod, these goddesses were the daughters of Zeus and Themis, and were therefore the sisters of the Horae (however, it is interesting to note that Hesiod also claims, in the same poem, that the Fates were the offspring of Nyx, the goddess of Night). The poet names the Fates as well:
"These are Clotho, Lachesis, and Atropos,
and they give mortals their share of good and evil."
(Hesiod, Theogony, 905-6)
Clotho was the spinner, Lachesis was the drawer of lots, and Atropos represented the inevitable end to life. This notion that human fate was spun around a person at birth by divine Spinners - in other words, the Fates - was popular in Greek mythology, poetry, and literature. Indeed, there is a compelling scene in the Odyssey of Homer that alludes to this concept of spinning fate.
In time, the somewhat vague idea of three goddesses who supervised the spinning of human fate evolved into a more concrete concept. The Fates came to be identified as a trio of older females who handled the threads of human life. One of these threads was allocated to every person, and each goddess took her turn in manipulating this thread. Clotho selected the thread, Lachesis measured it, and Atropos cut this thread to signify the end of a person's existence.
The Fates were known as Parcae (or sometimes, Fatae) in Roman mythology.
Who's Who in Classical Mythology