Clara and Eliza attempt to appear as ladies at Mrs. Higgins' at-home. Contrast their behavior to that of Mrs. Higgins in Pygmalion.
Pygmalion is the story of language and class and culture--both high and low. In this scene, unlike her son, Mrs. Higgins is polite and welcoming, despite the fact that Henry has surprised her with this "experiment." She is gracious in every way (even though she really tells it like it is to Henry), which is a wonderful foil for her son's behavior.
Clara is also a young lady of social standing (though no money), and she should know how to conduct herself in these kinds of gatherings. Instead, she's rude and disrespectful and very "teen-agery" in her behaviors. She's neither happy nor content, and everyone around her sees it. She acts like a petulant child.
Eliza is trying so very hard to be all that Mrs. Higgins is--but it doesn't go so well. She speaks way beyond the bounds of the subjects she was given, and she amuses them all with her slips into improper English. When they laugh, she gets a bit miffed at them, but she's pretty good-natured about the whole thing in the end. She has the right attitude but the wrong behaviors.
Neither of these young ladies is able to match the social grace and poise of Mrs. Higgins; however, by far the least socially acceptable behavior in the room is exhibited by Henry.