They take more space on the results page and get clicked more than a plain blue link. Google decides whether to show them, but it can only do so when the page carries valid structured data of the right type and the visible content matches it.
The types most often available to a business site are FAQ, Product, Article, Breadcrumb and Organisation details. A page with no structured data is ineligible for all of them, whatever its ranking.
Google's Rich Results Test shows in seconds whether a page qualifies, and which fields are missing when it does not.