It illustrates the success of professor Higgins in transforming Eliza as well as his failure in realizing she was developing a soul and mind of her own. Discuss with close reference.
Act IV has the crisis of Shaw's play, for it is the moment when the conflict presented in the first act comes to a head. In this act, the cirisis is the outgrowth of a conflict between Higgins and Eliza. After all the efforts that Higgins has made to have Eliza appear to be a lady, he yet perceives her as a "guttersnipe"; however, Eliza feels that she has undergone a change that leads to her identity crisis.
When we first put Higgins and Eliza together, I think we are waiting for the other shoe to drop. We just know that this is not going to work out, somehow. We are waiting for the time when they fail, because we don't expect them to succeed.
I believe you are correct in this assertion. Certainly it is the scene where Higgins and Pickering are able to rejoice in the success of their scheme. Eliza has been passed off as a high-born lady and thus Higgins has been proven correct. However, far more significantly, the importance of this scene lies in the way that Eliza finally asserts herself as a character in her own right. As she flings the slippers violently into the face of Higgins, note what she says:
You don't care. I know you don't care, You wouldn't care if I was dead. I'm nothing to you--not so much as them slippers.
Eliza finally releases her pent up frustration and anger at being objectified by Higgins. In response to being told by Higgins that she should marry, the answer she gives is significant in the way that it forces Higgins to radically reassess his own ideas of womanhood and what a woman can be:
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.
This of course marks the beginning of Higgins coming to realise that Eliza is an equal character in her own right rather than a mere, lesser burden. Thus we can see the importance of this act in terms of how it marks the "success" of Higgins' scheme to transform Eliza and also the assertion of Eliza's own character and how Higgins is forced to change as a result.