WordPress Search Functionality
WordPress search will query page titles, page content, single image titles and captions, image alt text and file names. It does not include widgets, comments, categories or tags. Searches are limited to the site.
Role of URI When Searching
By default, WordPress search URLs use a format of coresite.com/?s=search-term. This can be modified to be more user-friendly slug within the functions.php file by manipulating the mod rewrite ability.
Show Current/Active Search Term In Search Form Field
The function get_search_query() can be used to retrieve the contents of the search WordPress query variable. Search forms can contain this information to display the current search term.
Summary
WordPress has a built-in search function that limits searches to certain components of the site, but these can be expanded by using plug-ins.