Ovid's brief account of Apollo slaying the giant she-dragon (drakainan) at Delphi (Meta. I. 416.ff) serves to introduce the story of the pursuit of Daphne.
Delphi, the center (omphalos) of the Earth, is linked to Themis, a Titaness who had the gift of the oracle prior to Apollo. She is also the goddess of Justice, the second wife of Zeus, and the mother of Prometheus.
Another prime source lurking in the background of the scene of the slaying of the serpent is the Homeric Hymn to Apollo. This amazing poem is well worth reading for its own sake (there are actually two hymns - one to Delian Apollo, the other to Pythian ( ) Apollo, that are yoked).
According to this poem, the dragoness at Delphi raised Typhaon "to be a plague to men." This Typhaon was a monster that Hera bore, in spite, after Zeus birthed Athena, unassisted by his wife, the goddess of childbirth.
The hymn makes much of the fact that one of Apollo's epithets, "Pythian," relates to the word for the serpent. Not because it was a python, but because the Greek word putho means "rot" - which is what the remains of the serpent did after it was killed by far-shooting Apollo. From its decomposition came vapors that were believed to put the sibyl into a prophetic trance. From the word came the Pythian games, the original Olympics in honor of Apollo, that included music and poetry as well as athletic competition.