Featured search results are recommended links displayed on a search results page. This can be useful when trying to encourage users to a specific page. You could equate it to the sponsored links in a Google search.
A good example of it in use can be seen on Staffordshire County Council's website. They have a page entitled "Waste and Recycling". When you type "bins" into their site search, the "Waste and Recycling" link appears as a featured search result.