The search function in Wordpress is included in the Wordpress core. The Wordpress search function works like a browser search engine only on a more limited scale. The Wordpress search function searches the content from the titles and bodies of posts and pages. This leaves a lot of your content unsearchable such as widgets, comments, categories, gallery captions, and tags.
The URI is in essence the GPS location to what you are searching for. URI is a Universal Resource Identifier. It is an umbrella term that covers other locators such as URL's. The syntax of a URI is URI = scheme:[//authority]path[?query][#fragment]. Scheme is the protocol used to interact with the resource like https. Authority represents the host and port information. Path is well the path to find the resource and is usually made up of a sequence of segments seperated by slashes. And the final ingredient to the recipe is the query which is an optional string that contains a series of attribute-value pairs preceeded by a question mark. elegantthemes.com
I think get_search_query is what is used to accomplish this. I know that is what is used to display it in the h2 on our pages, but I can't find anything telling me how to add it to the search form.
Having search functionality is huge in creating a pleasant UX. While the default Wordpress search function is O.K., it is limited. There are plugins that will enhance the search functionality though. like ElasticPress, Swiftype, and Ivory. Ivory boasts over 100,000 active installations and maintains a perfect 5 star rating.