The Three Fates or the Moirae are responsible for determining the course of all mortal's life under Zeus order. They are daughters of Zeus and Themis, goddess of justice, younger sisters to Athena and older sisters to Persephone, Artemis, Apollo, Aphrodite, Ares, Discord and Hephaestus. In appearance, they are three women in various stages of life. Clotho or "the Maiden" the youngest sister spins a person's life thread, Lachesis or "the Matron" the middle sister measures the thread and finally, Atropos or "the Crone" the eldest one cuts the thread, thus ending the person's life.
As a general rule, the Fates work with the other deities to determine the proper times for a person's death and it seems that any Olympian of sufficient rank can order or delay the death of a mortal (such as when Ares ordered the Fates to cut Xena's thread if she interfered with Hope). Zeus's authority is the one the Fates hold in highest regard and Atropos will not cut the thread of someone under his protection. The Fates' connection to or relationship with Celesta is unclear, but it is possible that the rightful time for Celesta to collect a soul is when Atropos cuts it.
In spite of their membership in the Olympian pantheon and their respect for the authority of Zeus, the Fates are aware of events and destinies beyond the pantheon. Most notably, they were aware that the Twilight of the Gods was at hand and informed Zeus and Hera that there was nothing that could be done to prevent it. Later on, they gave Xena a cryptic clue as to how to kick-start Twilight and unsurprisingly, they did not assist the Olympians when the final battle began.
The fate of the Three Fates is unclear- after Gabrielle destroyed their loom to return history to normal, it is possible that they and their control over destiny ceased to exist, though since they survived Twilight in the first place, it is possible that they survived, content with their threads.
Powers and Stats
Age: Unknown, though one (Clotho) appears as a child, another (Lachesis) as a young woman, and the last (Atropos) as an elderly woman. All are likely many millennia old
Classification: Olympian Goddesses
Powers and Abilities: Immortality (type 4), precognition and some level of cosmic awareness, powerful and wide-ranging fate/probability manipulation, reality warping, can erase or restore memories (as seen when Ares used a thread to restore Hera's), time manipulation of various kinds (can alter the entire timeline of the world and they are immune to time stops), their presence can forge contracts into unbreakable bonds, transgression of which harms the transgressor, should they cut a person's life thread, that person will die (though the time of death may be delayed with the intervention of other gods)
Attack Potency: Planet level (should their loom be destroyed, the entire planet will be destroyed and reborn following a different timeline)
Speed: Unknown (possibly Faster Than The Eye+, but they were never shown in actual combat)
Lifting Strength: Unknown
Striking Strength: Unknown
Stamina: Essentially limitless
Standard Equipment: Their loom, which lets them manipulate the fate of the world
Intelligence: Vast knowledge of all the goings-on in the world, possible planetary omniscience
Weaknesses: None notable