The core search feature that WordPress provide is it will only search titles and the body of your post and pages. Some important content that it is missing includes comments, widgets, and tags.
The URI is the characters that will be used when the searching is occurring. It will look for title names and then base your search off content that is found and matches.
To get the search term to appear in the search bar you have to change the value to display the text that was searched, To do so you have to use is_search instead of
Overall WordPress search is a very useful resource provided and just basic functions made it very useable. You can add different plugins which will help made your searches more accurate and find more information.