Mrs. Higgins, Henry Higgins's mother, was once a young, intelligent independent woman with progressive ideas. When we meet her, she's older, but she's no less intelligent, independent, or progressive – well, maybe a little less progressive. In many ways, she's a traditional mother figure: she doesn't take any of her son's nonsense, and she does ask him why he hasn't married. At the same time, she knows a thing or two about being a woman in turn-of-the-century London, and she fears for Eliza's fate. After watching Eliza's performance at her little party, Mrs. Higgins tells it like it is to her son: Eliza's certainly a fine example of your art, she says, but you're just going to leave her in an awkward position. Eliza won't be able to support herself with the kind of skills you're giving her.
Mrs. Higgins's primary function is to raise these big issues, and to warn Higgins of the eventual, unavoidable consequences of his actions. By giving her a sharp wit and a bit of a motherly streak, Shaw makes Mrs. Higgins more than simply a talking head. There's a reason why Eliza runs off to Mrs. Higgins's place when she's had enough of Higgins: she's just the kind of cool older lady you want to run to when you need some good advice.