Short answers, pulled from the story.
The Moirai were the three personifications of fate and destiny in ancient Greek religion. Their role was to ensure that every being, mortal and divine, lived out the destiny assigned by the laws of the universe. Their Roman equivalents were the Parcae, also called the Fata.
Clotho, the youngest, spun the thread of each life from her distaff. Lachesis, the allotter, measured each person's thread with a rod. Atropos, the eldest, cut the thread with her abhorred shears; her name means the unturning or the inevitable. Their Roman counterparts were Nona, Decima, and Morta.
Moirai comes from moira, meaning lots, destinies, or apportioners, related to meros (part, lot) and moros (fate, doom). Scholars trace the root to the Proto-Indo-European *(s)mer, meaning to allot or assign, and a Latin descendant meritum may lie behind the English word merit.
Herodotus wrote that not even a god could escape the Moirai, and the Pythian priestess at Delphi admitted Zeus was subject to their power. Aeschylus argued that Zeus could not alter what fate had ordained. In later Olympian tradition, however, Zeus was described as their father and as giving them their greatest honor.
Three temples dedicated to the Moirai are documented: in Corinth, Sparta, and Thebes. The Thebes temple was imageless, the Corinth temple held statues not exposed to public view, and the Sparta temple stood next to the grave of Orestes. Pausanias also documented sanctuaries at Olympia and an annual festival at a grove of holm oaks near Sicyon, where worshippers offered pregnant sheep.
The Norse Norns, named Urdr, Verdandi, and Skuld, governed fate by twining the thread of life. The Lithuanian goddess Laima and her sisters Karta and Dekla, and the Hurrian Hutena, formed similar fate trinities. The Egyptian Maat and the Vedic Rta represent comparable concepts of cosmic order, and Shakespeare's Three Witches in Macbeth drew on both the Moirai and the Norns.