Hekate is a powerful triple Goddess of the moon, earth, and underworld. Perhaps originally a moon Goddess, Her name means "Far-Darter," which is a title also given to Apollo the (sometimes) sun God Whose rays are like arrows, and indeed She was often equated with His archer sister Artemis. Hekate is said to have come from Thrake, a land the Greeks considered barbaric, and most accounts name Her daughter of the Titans Perses (by some accounts brother to Kirke) and Asteria ("Starry," also an epithet of Aphrodite), both Deities of light. As the moon, Hekate (with Helios, the sun) served as witness when Demeter's daughter Korewas abducted, since the moon and sun see all.
As an earth Goddess, Hekate could grant wealth and riches. As Hekate Trioditis ("Goddess of Crossroads") or Trivia (the Latin form of the word), She protected crossroads, especially those where three roads met, and is shown in triple form standing back to back to back, sighting down each road. She also protected travellers, especially solitary ones in lonely places.
As Goddess of the Underworld Hekate was said to attend Queen Persephone (aka Kore), and associate with spirits, ghosts and hounds. She also had great powers of magic and witchcraft. On Earth, She was known to haunt tombs and places where crimes had happened, and was followed by Her ghostly train and spectral hounds. Though humans could not see Her, earthly dogs always could. Sacrifices were made to Her on the last day of the month in the Greek lunar calendar, at the dark of the moon.