In George Eliot's novel Silas Marner, Eppie is the child of Godfrey Cass and Molly Farren. Already, just by looking at her parents, we see how Eppie fits a specific role.
Remember, Molly is poor, and Godfrey comes from an esteemed family. Their marriage is secret. We might see Eppie as the result of a mixing of the classes. Eppie's role could be to remind us of their disastrous union. Yet her role also lets us know that just because disaster befell her parents, it doesn't mean that it has to ruin her life.
Eppie goes on to play a huge role in the life of the outcast Silas. Before Eppie, Silas didn't really have much of a social life in the village. After Eppie, Silas begins to socialize and make more of a personal investment in the village. We might say Eppie helps restore Silas's faith in humans.
We might also say that part of Eppie’s role is to help Silas realize that there's more important things in life than money. After living with Eppie, what does Silas start to believe? He begins to conclude "that the child was come instead of the gold—that the gold had turned into the child."
On a more contrarian note, you might want to discuss how Eppie's role reinforces rather limited roles for women in general. What happens at the end of the novel? Does Eppie go on a big adventure? Does she become a powerful titan of industry? No. She gets married. Where do the newlyweds live? With Silas.