Eliza comes very close to being a walking cliché.
She's the poor girl from the streets who turns out to be equal parts brilliant and beautiful. She's smart, independent, and feisty. She's a chocoholic who throws slippers when angry.
This sounds like a recipe for a cookie-cutter inspirational heroine, but, man, does Eliza have charm. For one thing, you can't hate a girl who howls every time she gets angry. Literally, she howls like a deranged wolf—here's a direct quote:
It should be said that a lot of the time Eliza functions as comic relief. Her howls, her indignation, her frequent exclamations of "Garn!" and "I'm a good girl, I am," and most notably her performance at Mrs. Higgins's party are all designed to make us laugh.
Throughout it all, however, we know that she's trying her hardest to achieve her goals. We feel for her when we realize that Higgins and Pickering are getting a little carried away with their experiments. By the time we get to Act 4, we're behind Eliza and, when Higgins ignores her, we're furious on her behalf.
By then she's gotten over all the things that made us laugh. She doesn't speak with a thick accent; her grammar is correct; she moves with poise and confidence. We here at Shmoop don't usually condone throwing slippers (or shoes of any kind), but we can only nod approvingly when Eliza throws a pair at Higgins.
Over the course of the play Eliza is transformed from a poor flower girl into a sophisticated young woman, but, perhaps more importantly, she stops being the butt of jokes and becomes a real three-dimensional character, someone we can really feel for.
Toward the end of the play we find out that she's not 100% confident—she starts up again with the howling—and that she's not all sweetness and light. She shows Higgins that she's proud and she's shrewd, and tells him that she doesn't want be married off to some rich guy:
HIGGINS [a genial afterthought occurring to him] I daresay my mother could find some chap or other who would do very well—
LIZA. We were above that at the corner of Tottenham Court Road.
HIGGINS [waking up] What do you mean?
LIZA. I sold flowers. I didn't sell myself. Now you've made a lady of me I'm not fit to sell anything else. I wish you'd left me where you found me. (4.63-66)
Like Higgins says, she is his equal, but she doesn't want to go his way or live his life. She'd rather go into competition with him than get hitched for mere financial gain.
On a thematic level, Eliza serves to show us how messed up society is. Her transformation is a testament to the power of education and language. Her difficulties demonstrate how little "the system" appreciates her kind of intelligence. She's an inspiration and a warning, and she's anything but a cliché.