Some say that Hekate is the daughter of Erebus and Nyx, ageless Goddess of the night, while others believe that She is one of the Furies or the last surviving Titan except for Zeus. Hesoid claims that She was born of the Titan Perses and the star goddess Asteria.

Historically Hekate probably originated in the mythology of the Karians in southwest Asia Minor, and was integrated into Greek religion around the sixth century BCE. However, there is evidence that Hekate evolved from the Egyptian midwife goddess Heqit, (alternatively spelt 'Heket' or 'Hekat'.)
The frog headed goddess Heqit assisted with the daily birth of the Sun and was associated with the apparently magical germination of the seemingly lifeless corn seed. In pre-dynastic Egypt the matriarch and wise woman of the tribe was called the 'heq'.

Hekate's name has several possible meanings. 'She who works Her will' is the most commonly accepted, but 'the distant one,' or 'most shining one' are alternative derivations. Representations from around the forth century BCE show a young goddess of both beauty & power, carrying a torch & wearing a headdress of stars. 'Hekate' is the female equivalent of 'Hekatos', an obscure epithet of Apollo, with whom She is sometimes associated.

The Olympians 'adopted' Her after they had defeated the Titans, but She was not of the same kind, & never lived amongst them. During this time Hekate's power was still recognized: Zeus gave Her dominion over Heaven, Earth & Sea, & they shared the right to grant or withhold gifts from humanity. Hekate was worshipped as Goddess of abundance & eloquence, & She is still generous to those who recognize Her.

Hekate is sometimes referred to a triple goddess. Classically She was part of a group with Persephone and Demeter. Contrary to modern Pagan assumptions, Demeter represents the old crone woman, Persephone the wife woman, and Hekate is the Maiden. Every early Greek representation of Hekate shows Her as a young woman. It is only much later that She is represented as Crone.

In Mytilene on the eastern coast of the Aegean Sea, near what was Troy, there were Temples of Demeter, where the women would go to the annual festival of Eleusis to celebrate fertility Rites. There is ample evidence that Hekate was honored there too, perhaps as a guide for initiates into the Mysteries.

But Hekate's power was to fade. In later myths She is represented as a daughter of Zeus who rules the Underworld & the waning Moon. The Greeks began to emphasize Her darker aspects; Hekate as Goddess of the Dead & Queen of Witches. Now She roams the earth on moon less nights in the company of baying dogs and the hungry spirits of those dead who were not ready to die, those who were murdered or not given appropriate burial rites.

The Romans adopted Hekate, and Her role shifted again. Hekate became an aspect of the moon Goddess, Diana Triformus: Diana (the Full moon, associated with Earth), Proserpina (the lunar phases, associated with Heaven), and Hekate (the New moon, associated with the Underworld.)

As the power of the Solar Gods rose, Hekate became increasingly demonized, until by the Middle Ages She was reduced to a parody of an evil crone.

Source: http://www.hecate.org.uk/history.htm