What role do women have in this book?

Ovid's Metamorphoses is an epic narrative poem. Since the poem includes fifteen books and a wide cast of over two hundred characters, it's tricky to generalize about the role of women. But we can certainly point out a few overarching themes.
Objects of desire (and victims of violence)
Throughout the text, women are objects of male desire, whether they want to be or not. In fact, women spend a lot of time trying to escape men or defer their advances, often unsuccessfully. Jupiter, the king of the gods, is lustful and aggressive, and he rapes many women in the poem, like Io and Europa. Apollo tries to rape Daphne, and he kills his lover Coronis in a fit of passion. Dis rapes Proserpina. The list goes on.
Mothers
One of the most important roles that women play in the poem is as mothers of other important characters. Fertility and reproduction are key values here. Venus, for instance, gives birth to Cupid and Aeneas. Thetis is the mother of Achilles.
Symbols of wisdom and strength
Some women in the story get to do something other than reproduce or run from the men who are trying to pursue them. Minerva, for instance, is the goddess of war, art, science, and wisdom, and she is the designated protector of Athens.
Catalysts of revenge
Revenge is a major theme in the Metamorphoses. This is best embodied in the Furies, three sisters who are actually goddesses of revenge. But many female characters act in revenge in the story, shaping the course of the narrative. Juno is always trying to find and punish her husband's lovers; Diana turns Actaeon into a deer as revenge for the fact that he saw her naked; Minerva turns her rival, Arachne, into a spider; and so on.