The site search box, which appears under the search results for some sites, lets you restrict your search to the selected site. For example, if the search box appears under the result for www.example.com, typing
peanuts in the site search box will search the site www.example.com for the word "peanuts". It's the same as performing a
site: search, like this:
peanuts site:example.com.
The site search box makes it easier for users to refine their searches, and our experiments have found that this makes it faster to find the exact page they are looking for.
Webmasters don't have to optimize their sites to make the site search box appear. We don't display this box for all sites, but only when we determine - based on our user search data - that it would be useful to our users. As we refine this feature, the sites for which it appears may change.
You can also try
other web search features supported by Google.