A fast website gives visitors good user experience, whereas a slow website does not. Humans don't like waiting, especially seeing it contributes to a lousy user experience.
Conversion is closely correlated to page speed. Various studies show that every extra second can cost you money. Therefore, slower speeds mean less conversion, whether this is a subscription to your newsletter or the purchase of a product.
Google, too, likes fast websites. Speed is a ranking factor and has a direct influence on SEO (search engine optimization).