Google Search Console is a free web service from Google for the owners of websites. It reports how Google Search sees a site: which pages Google has crawled (read with its automatic program) and indexed (stored, so that they can appear in results), and how the site performs in the results.
The Search Analytics part, the Performance report, lists the search queries that bring users to the site, with impressions (how often a page was shown), clicks and average position for each query. The owner can submit a sitemap (a file that lists the site's addresses) or single URLs for crawling. The URL Inspection tool shows the crawl, index and serving data that Google holds for one page. Email alerts report indexing, spam or security problems, and other reports cover Core Web Vitals (page speed measures), structured data for rich results, and the sites that link to the site.
It runs in the browser and needs a Google account and a verified claim that the user owns the site. The service is free; a site does not need it to appear in Google Search.