You likely know the basics of Delphi: Dedicated to Apollo, it was an oracle, a place people went to ask the gods a question about what they should do and listen to the answer given. There were many such sites in ancient Greece, but this was the center of the world, so determined by Zeus. It was the most important oracle.
Like all serious religious phenomena, however, as you dig deeper you discover that it is difficult to figure out what "really" happened. Did the priestesses who gave the oracles do so by means of trance-inducing vapors issuing from rocks, by means of hallucinogenic drugs or not at all? Did the male priests change priestess' ramblings to serve their own agenda or did they merely order the ambiguous divine words and help seekers to understand? Was it all just politics and intentional conning of the gullible? All of these theories and more are in circulation.
Ultimately, your view of religion and the possibility of 'the beyond' will have a large influence on your view of Delphi: if your faith is in reductionism, you'll only accept a mundane explanation for the oracle; if your faith is that the universe has meaning, you'll want to find an explanation that preserves some mystery. Either extreme, however, shortchanges the need to find an explanation that fits both the complexity of human motivation and the complexity of the universe so say nothing of the actual evidence we have.
Even more intriguing about Delphi is that most of what “everybody knows” about the place is likely at least partially wrong. The priestess oracle was not a simple peasant girl, there was more than one of them operating at any given time, there’s pretty much no evidence she didn’t give seekers the oracle herself, and many oracles were not ambiguous at all.
And while there is no cavern under the temple, just at the turn of the millennium was it discovered that intoxicating fumes do come from fissures in the rocks where two faults meet under Apollo's temple.
The shrine accepted bribes on more than one occasion to deliver oracles in a desired direction or another, but at the same time, it was revered and consulted by Greeks and Romans of every station in life including kings and other leaders.
The setting of Delphi is beautiful. Nested against the southern slopes of Mt. Parnassos, it is a fit setting for religious mysteries and the rugged climb into the hills a suitable preparation for posing a question to the gods.