Shaw took the title of his play from an ancient Greek legend. According to this legend, Pygmalion was a sculptor who disliked women and did not see any reason to ever get married. Nevertheless, Pygmalion grew lonely and decided to create an ivory sculpture of a beautiful woman. This sculpture was so beautiful, in fact, that Pygmalion fell in love with it.
Shaw's Pygmalion therefore reflects this legend and the title pays homage to its message. At the beginning of the play, Profession Henry Higgins has negative views of women, just like Pygmalion. He believes that women are a "damned nuisance," for instance, who "upset everything" when they enter a man's life.
Similarly, by receiving elocution lessons from Professor Higgins, Eliza becomes a symbol of Pygmalion's sculpture. At the start of the play Eliza is a flower girl but, by the end, speaks as well as any duchess. She is indeed a creation of Professor Higgins, just like Pygmalion's beautiful sculpture.