Search Box is a SERP Feature on Google. It displays for certain websites after users search for certain keywords. The Search Box is essentially a small search box, like the browser search box itself, which is situated underneath an individual web listing. It allows web users to search the contents of that website directly from the search engine results page.
When a search is made in Google’s Search Box, there will be one of two outcomes. One option is that the results of that search will be displayed as a set of Google results. The second is that the search will take the user through to the website being searched, where results listings will be displayed.