Pygmalion is a Greek name. In Greek mythology, Pygmalion was a sculpture who carved a statue of a beautiful woman out of ivory. The statue was so beautiful, that Pygmalion fell in love with it. The symbolism in the play has to do with Henry Higgins falling in love with his own creation. Liza Doolittle was an uneducated cockney whom nobody could really understand when she spoke. Higgins, a professor of linguistics, believed he could train her to talk and act like a lady and he then fell in love with his creation. The theme of the play has to do with social status, relations between men and women, the nature of beauty, the nature of reality. You can read about the play here on eNotes.