The role of the Moirai is to control the fate of every being. The life of each being is represented by a "thread of life". Clotho spins the thread, beginning the being's life. Lachesis measures it (looks how long it is) and Atropos cuts the thread at the end of the person's life once they have reached their destiny, killing them.
The Moirai are considered to be above the Greek gods. However, in some stories, Zeus, the Chief God, is capable of controlling them.
The decisions of the Moriai about a person's life cannot be changed.
The parents of the Moirai are not surely known. Some said they were the daughters of Zeus and the TitanessThemis, or more likely of primordial beings like Nyx, Chaos or Ananke.