In Rosemary's Baby:
She asked him questions that had been unspeakable in Catholic High; he sent her to a night course in philosophy at NYU. “I’ll make a duchess out of this cockney flower girl yet,” he said, and Rosemary had had wit enough to say “Garn!”.
What does the word "garn" mean?
For the direct meaning of the word, you can check for example Wiktionary:
From go on.
Interjection
garn
(Cockney slang) A response that expresses disbelief or mockery.
The example quote provided in that Wiktionary page is from George Bernard Shaw's play Pygmalion, which was adapted into a famous musical and later an award-winning film both titled My Fair Lady. The story is about a linguistic professor who teaches a Cockney flower girl to speak "proper" English in order to pass her off as a duchess - the passage you quote from Rosemary's Baby is a direct and clear reference to this. Quoting from the play Pygmalion itself (emphasis mine):
THE FLOWER GIRL [tickled by the performance, and laughing in spite of herself] Garn!
THE NOTE TAKER. You see this creature with her kerbstone English: the English that will keep her in the gutter to the end of her days. Well, sir, in three months I could pass that girl off as a duchess at an ambassador's garden party. I could even get her a place as lady's maid or shop assistant, which requires better English. That's the sort of thing I do for commercial millionaires. And on the profits of it I do genuine scientific work in phonetics, and a little as a poet on Miltonic lines.
You can also listen to the line "Garn" from the film adaptation, and read more about its meaning from our friends at the English Language & Usage Stack Exchange.
In the passage you quote from Rosemary's Baby, it seems that Hutch is trying to raise Rosemary's intellectual and social level - responding to "improper" question by sending her to philosophy classes. He likens himself to Henry Higgins, the linguist who trains flower seller Eliza Doolittle to speak like a duchess. Rosemary has wit enough to reply in kind, saying "Garn!" in Eliza Doolittle style.
