WebSite (schema.org) & Sitelinks Search Box
The schema.org type WebSite describes a website as a whole, with its name and URL. Combined with the SearchAction property it additionally declares the URL template under which the site's internal search can be reached.
In practice
An important note on status: Google's sitelinks search box, which this markup was originally intended for, has been gone since November 2024 – Google removed the feature from search and deleted the corresponding documentation page. Marking up WebSite with SearchAction therefore no longer produces a search box in the results.
The markup is still worth having: it is valid schema.org and tells any system that wants to search a site deliberately – increasingly AI assistants too – in machine-readable form how the internal search is called. As before, the prerequisite is that this search really exists and its results are reachable through a URL parameter. Anyone who planned the markup purely for the search box can save the effort.