The Rundown on Google Sitelinks Search Box
Google sitelinks are an excellent way to let your website's listing stand out on the search results.
In early September (2014), the search engine released a "new and improved" sitelinks search box which will enable users to reach specific content on a website directly through your own website's search pages.
When Google determined that a user was looking for something specific on a website in the past it would show a large set of sitelinks and an additional search box below that result. The newly released search box appear above the sitelinks, supports Auto-complete, and will even send the user to your own website's search pages (when you use the right code).
In order to get take advantage of this feature, it's neccessary that websites have site-specific search functionality in place on their site. The next step is to mark up the website's homepage as a schema.org/WebSite entity with the potentialAction property of the schema.org/SearchAction markup (JSON-LD, microdata and RDFa are supported).
An JSON-LD example of the schema.org markup:
Once implemented, users will be able to jump directly from the sitelinks search box to a site's search results page. When Google is unable to find any markup, the search engine indicated that it would show its own search results page (which means competitors ads are likely to show - so take that into consideration if you're not going to impliment the sitelinks search box code.
Google indicated that they've seen an "enthusiastic uptick" in the markup implementation, and addressed a few issues it's seen since the initial announcement was made. Google advised webmaster to make sure when they replace the curly braces (and what's inside) with a search term it leads to a valid URL on the site, and to make sure that the "query-input" field points to the same string inside the curly braces in the "target field."