Epithets are other names that a god is known by due to regions they were worshipped or/and divine associations. The Hellenic Theoi (Greek Gods) have many epithets except for Hestia who due to information about her cults being lost means she has no known epithets; the info we know is that she is a daughter of Chronos and Rhea, is the goddess of the hearth (one of the house gods), never married (one of the virgin gods), and that she gave up her place as an Olympian for Dionysus.
On the other hand, Zeus (for example) has fifty-one epithets that are derived from his divine functions as god of weather, governance, the king of the gods, god of fate, giver of plenty, god of marriage, hospitality, protector of strangers and suppliants, protector and deliver from evils, purification, protector of freedom, and defence in war. (http://www.theoi.com/Cult/ZeusTitles.html)
While the god Apollon had thirty one as god of oracles, archery, music, healing, the averter of plague and evils, the protector from harm (from wolves, plagues of mice & locusts, mildew; protection of streets, entrances, embarkations, voyages, etc), and hunting.(http://www.theoi.com/Cult/ApollonTitles.html)
What these epithets do is show us what the god is associated with, and where they were worshipped more seriously.