A search engine is a tailored search experience that allows you provide customised search to your site's users. AdSense allows you to add a search engine to your site and earn by displaying AdSense ads on the search results pages.
If you want to customise the appearance of the search box and search results that you display on your site, you can use Programmable Search Engine. With Programmable Search Engine you can also refine the search results to make it easier for your users to find the information that they're looking for on your site.