Describe WordPress search functionality
WordPress's search bar searches within the website and it brings back post and page results that best match the term searched for. Some websites have a Google search bar that bring back results from outside the website, but WordPress's default search is for content within the website.
Explain the role of the URI when searching
The default role of the URI is to appear in the URL bar showing "s=searchkeyword" for whatever keyword is searched in the search bar. The "s" represents that the function is a search. The keyword is matched to pages and posts in the website. The format in the URL bar can be overidden by adding some code to the functions.php theme file, but the search will still work the same.
Explain how to show the current/active search term in the search form field
After searching for an answer on this, it sounds like there is more than one way to do this. Code can be added to the search.php file, funcitons.php file, or possibly another file. Some resources mentioned a searchform.php file or a plugin.
Summary
Overall, I think WordPress's search functionality is very good. I personally don't like it when websites have the Google search bar. It doesn't really help me find what I'm looking for on the website when it directs me away from the current website. WordPress's search bar can also be customized with plugins, code additions in the theme files, and the search URL can be made more user friendly.