We can cover these two women at the same time. They're always together, after all. (You can read more about Clara in the "Character Roles" section.)
And they really just represent two stages of what Shaw calls "genteel poverty." They're a mother/daughter team of reasonably wealthy ladies. They start the plot going when they ask Eliza if and how she knows Freddy.
They represent everything that Eliza is not: they're clean, well-dressed, and well-spoken. In the third act, we find out via Mrs. Eynsford Hill that the family isn't doing so well, and that Clara really doesn't get it. They're on the decline while Eliza's on her way up, and they're all headed for the same, uncomfortable middle ground...or at least middle class.