Google has introduced a new and improved sitelinks search box within the search results, making it easier for users to reach content on your site directly through your site-search pages.
When users are searching for a company, they might be looking for something specific on that website. Till now, Google would display a large set of sitelinks and a search box below that search result, allowing users to do site: searches in the site directly from the search results page. For eg: site: example.com hitchhiker guides.
Google has made this search box more prominent now. The search box is positioned just above the sitelinks, supports Google Autocomplete algorithm and takes you directly to the searched page if you use the right markup.
In order to markup your own site you must have a working site specific search engine for your site. In case you already have one, let Google know about it by marking up your homepage as schema.org/WebSite with potentialAction property of schema.org/SearchAction markup. Use JSON-LD, microdata or RDFa to do this.
Implementing the markup on your site will let users go directly to your site’s search results page right from the sitelinks search box. If there is no markup, Google will show the search results page for the corresponding site: query.