What the poem is about:

how at first you [Apollo] went
all over the earth
looking for a place
for your oracle for mankind

So, Apollo basically roams the earth looking for a place for his oracle. And I mean all over. He checks out at least 15 different spots, even making a few false starts. Finally, he comes to Delphi:

…Crisa
under the snow of Parnassus,
the shoulder of the moutain
turned toward the west,
where a ledge projects overhead,
and a hollow, rough, glen
runs underneath.

Apollo decides to put his oracle here, saying,

“It’s here that I’m inclined
to build a very beautiful temple,
an oracle for mankind,
where everybody will always bring
perfect sacrifices, whether they live
in the rich Peloponneseus [Greece]
or in Europe, or in the islands
that are surrounded by waves,
because they will be looking for oracles.
And I will give out oracles
to all of them, accurate advice, too,
I’ll give it to them
in my rich temple.”

So, Apollo’s goal here is to build a universal oracle.

Soon we come to the bit about Python. (I wish this edition had line numbers.) Lines 300ff.

But near this place there was a spring
that was flowing beautifully,
and there the lord [Apollo], the son of Zeus,
killed the big fat she-dragon,
with his mighty bow.
She was a wild monster
that worked plenty of evil
on the men of earth,
sometimes on the men themselves,
often on their sheep with their thin feet.
[I'm guessing this means that she ate their sheep.]
She meant bloody misery.

Then the poem goes on for many, many lines (a couple of pages) about how Hera bore Typhaon in retaliation for Zeus “giving birth” to Athena without her. Although this is the alternative account of Typhaon’s origin, in both accounts the father is Tartarus, and the creature in some way comes from the earth, with Gaea as its mother in Hesiod’s account, and Hera becoming impregnated when she called upon Gaea and the other Titans to give her a child in the Hymn.

Hera gives Typhaon to the “she-dragon” at the spring, who “used it to do / plenty of terrible things.” (lines 350ff.)

Whoever encountered the she-dragon,
it was doomsday for him,
until the lord Apollo,
who works from a distance,
shot a strong arrow at her.

Then we get a lovely description, in gory detail, of the death of the snake, with Apollo saying, “Typhaon won’t save you.”

And here comes the questionable etymology of Pythia (lines 370ff.):

And the sacred power of the sun
rotted her out right there,
which is why the place is called Pytho (rot),
and why they give the lord
the name of Pythian, because it was right there
that the power of the piercing sun
rotted the monster out.

I’m including the bit about Typhaon because the story of Apollo’s victory over these beings represents the ascendancy of the Olympic pantheon, the gods of Homeric, heroic Greece over the older, chthonic gods of the substrate religion.

Why does any of this matter? Well, from this, we get that the Pythia is older than the Olympian tradition, predates the worship of Apollo at Delphi. It means that the Pythia’s origin is in the chthonic tradition of Greek religion, a tradition more readily identified with ideas of female sacredness and divinity.

The chthonic era of Greek religion was mostly about making sure to appease the spirits of the dead and the lords of the realm of the dead. It was about fear. The snake, according to Gilbert Murray in his Five Stages of Greek Religion, is “a well-known representation of underworld powers or dead ancestors.”

So, we have a female conduit of the divine, who channels the breath of the underworld (later the pneuma of Apollo)—the vapors she breathed in from the crack in the earth over which she sat. In the ancient Greek world, for whatever reasons, the female was alien and scary, a power that was dangerous if untamed. She had a closer relation to nature, which is powerful, mysterious, and unpredictable.

So, when the Olympic gods came to Delphi, Apollo killed the resident deity, tamed the female servant of that god, and absorbed her into Olympic tradition.

(It is through of this assimilation of local chthonic deities that the Olympians come to have so many attributes. Apollo, for example, is sun god, god of prophecy, music, archery; he could both cure the sick and visit plague upon a people.)

(edition: The Homeric Hymns, Second Edition, trans. Charles Boer. Spring Publications, Dallas Texas, 1970.)

Reading:
Prolegomena to the Study of Greek Religion, Jane Ellen Harrision
Five Stages of Greek Religion, Gilbert Murray
Homeric Hymns, “The Hymn to Pythian Apollo,” trans. Hugh G. Evelyn-White

UPDATE:
Ugh. I’m such an idiot. Perseus does have the English translation. Gah! And it has line numbers.

I’ve added in some line numbers. They correspond with the lines in Greek.

Oxford Classical Dictionary (1961 edition):

Apollo (5)
Apollo’s earliest adventure…was the killing of Python, a formidable dragon which guarded Delphi (in the earliest version, the Homeric Hymn to the Pythian Apollo…, it is a female and unnamed).

Apollo (4)
Of his oracular shrines, Delphi was the chief…. The method of divination was by possession, the medium…being filled with the god, or his inspiration [literally, in Latin, breath into]…. Of his ritual perhaps the most remarkable was the Delphic Stepteria, held every eight years. In this, a boy, apparently personating [sic, it's a British book] the god, was led to a hut near the temple, called the palace of Python (see below). This was set on fire; the boy went away into supposed banishment; and finally all concerned were purified at Tempe and came back by the traditional sacred route known as the Pythian Way (see Farnell, 293). The ancients regarded the ritual a sort of play commemorating the killing of Python…. Delphi, through the enterprise of its clergy, became the nearest approach to a Vatican [and by this they mean its wealth as well as its authority, notes on that later] which Greece possessed, though it had no formal authority to enforce its advice. Delphic propaganda may be traced in the tendency to introduce Apollo as adviser, inspirer, etc., into any and every myth which contains a prophet or a prediction. Delphi claimed to be the centre [sic] of the world, the famous stone called the omphalos (navel) marking the very spot. In art, Apollo is often represented as sitting on this, but the actual seat of his medium, the Pythia, was a tripod, hence continually associated with Apollo and his oracle.

Notes to Self:
Python=snake and female: snake=underworld (god or spirit?), female=possible earth/Gaea religion which brings us to Prolegomena to Greek Religion and the older, chthonic religions)

Apollo killing Python represented the chthonic religion being replaced/defeated (outside? was Delphi conquered, or was it just a cultural shift through spread of new/different/Greek culture)

see entries for:
treasury
Delphic Oracle
Python
tripod

Add quote the Homeric Hymn in question [too lazy right now, time for bed; is on internet in several places anyway]. You might be able to find it at the Perseus Digital Library, the bestest source for classics but absolutely impossible to access because of loading time—I’ve been trying to get into Collections, Greek and Roman Materials the entire time I’ve been typing this note, and I am an extremely bad and slow typist. It’s actually much easier to look up a title or article than to use the search function.

Oh my god, it has actually loaded (after about 3 or more minutes). Yes! The Homeric Hymns are indeed there, but now I have to wait for that to load. Looks like I might as well quote it now since I’ve spent all this time on it already, if, that is, it loads within the next 5 minutes.

Path to get to Homeric Hymns on the Perseus Digital Library: Collections->Greek and Roman Materials->Homeric Hymns->Hymn to Apollo and page down about 8 times.

Ok, well, it’s only available in Greek, though there are notes in English (top of page, left, show). Perseus usually has both original language and English translation, but apparently not in this case.

UPDATE:
It was definitely time for bed. Perseus does have the English translation.

Mystery Cults

Mithras – primarily male followers

Dionysus – bacchae/maenads

Cybele & Attis

The Eleusinian Mysteries–Demeter and Persephone

And the Jesus Cult? Look at it in terms of early martyrs, e.g. St. Perpetua, as well as accounts of gatherings.

Beauty is terror. Whatever we call beautiful, we quiver before it. And what could be more terrifying and beautiful, to souls like the Greeks or our own, than to lose control completely? To throw off the chains of being for an instant, to shatter the accident of our mortal selves?

–Donna Tartt, The Secret History

This is a very interesting article that discusses Achilles and his fate in the context of the nostoi theme of the Homeric epics.

UPDATE: And is unfortunately gone, and I didn’t even download it. Maybe someday I’ll search for it in the hope that it has only moved. This is very distressing.