Shaw wrote Pygmalion in 1912, but he took its name from something way, way older: an Ancient Greek myth. The most famous of its many versions can be found in the Roman poet Ovid's Metamorphoses.
In the myth, Pygmalion, a sculptor from Cyprus, hates women, and especially hates the idea of getting married. Still, he gets tired of lying in bed alone at night, and decides to carve a beautiful woman out of ivory, a woman so beautiful that he can't help but fall in love with her. Which is exactly what he does. After making the sculpture, he can't help himself, and he kisses her and starts dressing her up and doing anything he can to make her seem more human. None of that helps to turn her into a human being, but he can't let her go. So, when the feast of Venus rolls around, he prays and begs and pleads with the goddess Venus to please turn this statue into a real live woman. Venus, sympathetic, or maybe just sick of Pygmalion's whining, grants his wish. When Pygmalion tries kissing the sculpture again, she starts turning warm and fleshy, and soon enough she is a real live woman. Pygmalion and his statue/woman get married, have a kid, and live happily ever after.
Pygmalion (Shaw's play) isn't a simple retelling of the myth, but it's pretty clear who's who here: Henry Higgins is the sculptor, Eliza Doolittle his creation. Shaw adds a lot more to the mix – stuff about British society, and women – and it's science, not Venus, doing the transforming, but the basics are the same. Just remember: there's a reason it's called Pygmalion and not My Fair Lady. It's about the relationship between Henry Higgins and Eliza Doolittle, but we have to pay attention to the old sculptor as much as we have to watch the beautiful statue coming to life.