What is Madame Ratignolle as a person, how is she a relation to Edna, and who or what she represent in The Awakening?

In addition to the previous answer, it is important to understand that Madame Ratignolle is serving as a character foil for Edna Pontellier. A character foil is a character who, when juxtaposed against the protagonist, elucidates opposite values while maintaing equal level (peer-like qualities) to the protagonist.

Edna is individualistic, self-proclaiming that she would "never give up herself for her children." She seeks to paint, swim, have visitors, make visitors, enjoy the company of men, and to be free of all constraints put upon her by society -- including a husband and children.

Madame Ratignolle, like Edna, is married with children, but that is the extent to which they are similar. Ratignolle seeks to serve her husband and her children, and is in fact the one who entreats Edna to "think of the children" at the end of the novel when Ratignolle can sense Edna's disdain for her own life. Ratignolle also refrains from attending parties, including Edna's party to celebrate her own living arrangement, and Ratignolle is unenthusiastic about visiting Edna's new apartment because of the possible rumors that exist regarding Edna's and Alcee's relationship. Edna searches for herself through defiance, while Madame defines herself through obedience.