In Act 2 of Pygmalion, what qualities does Liza reveal by coming to Higgins for a lesson?
In this world of distinct social classes, language is one of the determining factors as to which class one belongs. Because Eliza is a flower girl and speaks like one, she is seen as being of low class. The only hope she has of moving up the world in any way is to change the way she speaks.
When the opportunity is haphazardly offered to her, she dismisses it without much thought. She's more concerned with selling the rest of her flowers. Overnight, though, Eliza changes her mind and goes to see the Professor about the lessons he offered. We learn a lot about her just by looking at this decision she makes.
First, she is motivated to improve herself. She also has a good memory. Higgins's address was simply given in passing, yet she remembered. She managed to make her way to the house--which was far enough that others were taking cabs. Eliza has done her best to clean up, though she's still pretty bedraggled. She's good at math; she's figured not just the simple calculations but a more complex reasoning process whereby she knows what lessons must cost compared to French lessons. Finally, she is not daunted by approaching a Professor--probably because she recognizes she has more class than he does!