Prominence refers to how well-known a business is. Some places are more prominent in the offline world, and search results try to reflect this in local ranking. For example, famous museums, landmark hotels, or well-known store brands that are familiar to many people are also likely to be prominent in local search results.
Prominence is also based on information that Google has about a business from across the web (like links, articles, and directories). Google review count and score are factored into local search ranking: more reviews and positive ratings will probably improve a business’s local ranking. Your position in web results is also a factor, so SEO best practices also apply to local search optimization.