A Myth:
There is a big problem for any study of Greek Myths--they exist in the original literature as allusions in many cases. Aside from Homer, the few tragedies left, and a few works like Apollodorus, or Apollonius, we have to work not with full tellings of a myth, but with various allusions--the stories were so well known that there was no felt need to tell them in full. That is why there are so many handbooks of mythology in antiquity and in modernity.
What is grouped under the term myth is varied and most one-line definitions fail to capture some aspect: myth is the reaction of humans to the world around them and an effort to record the inner realities, but it is also many other things. It is also part of the human effort we call science to determine the causes of things, but not all myths are about causes--studying myth is often a messy business, and when we speak of mythology, it is hard to say what exactly we are speaking of.
A myth is a story, but not just any story: it is a traditional story. It is not fictional in the sense that someone made it up as, for example, Douglas Adams made up the plot of The Hitchhiker's Guide to the Galaxy. Rather it is fictional in the sense that it never actually took place. It is not history, although some myths are not purely fictional, but have some historical basis. The Trojan war is one such instance. All traditional stories are not, however, myths, for Aesop's fables are traditional stories, but are nonetheless not myths, although some traditional tales with clear morals are certainly called myths. We might be tempted with many anthropologists to think that myths concern the sacred, but it is unclear how myths about Hercules or Jason or Achilles, for example, are all sacred, or how the castration of Kronos is "sacred." We might want to divide what are traditionally called "Greek Myths" into "divine myths" and "heroic sagas." Thus we can preserve the "sacred" elements in the term myth.
Divine myths and heroic sagas both contain divinities, but Some Greek "myths" have nothing whatsoever to do with divinities. They have strange creatures like centaurs or minotaurs, but those are not divine. They are fantastic. Perhaps we need another category for fantastic tales.
It should be noted that in one sense what we study are not myths at all, with the possible exception of the Iliad and the Odyssey, because they are written down. A myth is essentially an oral creation: you cannot creat a mythology in writing. It must come to be before writing. The Myths of the aborigines of Australia, for instance, are orally transmitted in a culture without writing. In an important sense, the Greek Myths are the result of an interaction between the beginnings of literacy or its full bloom and a traditional, non-written, oral culture. When Apollonius, for instance, wrote his poem, he reflected it through a massive pile-up of versions which he could consult in texts.
As you read Hesiod's Theogony, consider what the individual gods are: are they really people? Do they have childhoods? Do they do anything? Consider how "gods" like Nemesis, Force, Night, and Sky differ from gods like Zeus, Aphrodite, and Ares. Also consider what role genealogy plays in the myths. What does it mean for Earth to have children? What characterizes all the children of Night? Consider that Hesiod probably knew several variants of each myth that he put into his system.