Eliza is the free black who works for the family, she is an excellent cook and Mattie considers her to be a friend.  But, more than that, Mattie has a close relationship with Eliza, more like a mother and daughter.  This is significant since Mattie does not have a close relationship with her own mother.

Eliza was the coffeehouse cook. Mother couldn't prepare a meal fit for pigs. I found this amusing, considering our last name was Cook. In a manner, though, it was serious. If not for Eliza's fine victuals, and the hungry customers who paid to eat them, we'd have been in the streets long ago. Mother's family had washed their hands of her when she ran off to marry a carpenter, a tradesman (the horror!), when she was but seventeen. So we were very fond of Eliza." (Anderson)

Eliza is a trusted confidante and Mattie relies on her and because of their close relationship, Eliza helps Mattie to grow up and become more confident and secure in herself.

"Eliza befriends Mattie. She asks Mattie to work alongside her as an equal, thus giving Mattie the opportunity to further realize her self-worth. She does not interfere when Mattie makes her own decisions, helping Mattie mature to the woman she is quickly becoming."

Eliza is important to the plot, because the book concerns Mattie growing up and learning how to be self sufficient, and Eliza contributes to this process with her supportive friendship.