The Oracle of
Apollo at
Delphi was the most important religious centre in
Ancient Greece. It was one of the first centres of either worship or learning to gain
Pan-Hellenic influence, and as such had a lot of influence and power over the various
city-states.
Before the time of the Hellenistic gods and their enlightened, rationalistic ways, there was another oracle at Delphi - and in fact the mountain it is in the shadow of, Mount Parnassus, has been of sacred importance to the Greeks since time immemorial (Prometheus is said to have been chained to the top of it as his punishment in one of the earliest of Greek myths). The previous oracle was that of the earth-mother goddess Ge, and Apollo is said to have slain the guardian of her sanctuary, a giant she-dragoness, a violent deed for which he paid a heavy penance of fasting and purification. This story of a male god banishing and obliterating an earlier female deity is tied in with a trend of other such myths all over the Near East and the Mediterranean basin, as the advent of civilisation was forcing primordial fertility goddesses to the margins and bringing more modern, cerebral male entities to the forefront.
Apollo's Oracle itself was a woman, the Pythia (no doubt taking her name from the slain dragoness, the Pythos), who sat in a small dark cave at the back of the Temple of Apollo, not far from the spot which was then considered to be the centre of the world. According to Herodotus, the Pythia was seated on a tall tripod stool and spoke in a trance, serving as a vehicle for the gods' answers rather than giving her own. The trances were said to be induced by gases seeping through the bedrock underneath her seat, and her indistinct murmurings were interpreted by the priests of Apollo serving in the temple, who rendered them in verse and presented them to the supplicants. However, recent research suggests that the Pythia was less of a figurehead and in fact spoke quite clearly to the supplicants themselves. Furthermore, there are no vaporous crevasses at the back of the temple where her niche was situated.
Statesemen, powerful individuals, and even whole cities, represented by their elders, came to consult the Oracle before making decisions in important affairs of state. Her influence was thus almost boundless, but history seems to indicate that for the most part the Pythias and their servant priests used that power well, and Delphi was a hub of unifying, rationalistic, peaceful interaction between the city states of ancient Greece for most of its existence.
Sources:
http://www.lfc.edu/academics/greece/DelphiTour.html
http://www.arthistory.sbc.edu/sacredplaces/delphi.html
http://www.omegaresearchgroup.com/quest/d/delphi.htm