Google Search Console is a free tool from Google that shows you how Google sees your website, rather than how you hope it does. It tells you which of your pages Google has actually added to its index, which search terms are bringing people to you and how often they click, and where Google has run into problems it wants fixed. It is the first place I look when something goes wrong with a site's search rankings, because it reports the issue from Google's side instead of leaving you to guess. Setting it up takes a few minutes and proves you own the site; after that, it quietly collects data you can come back to. If your developer says "Search Console is showing coverage errors" or "your clicks dropped last week," this is the tool they mean. Every site I work on gets connected to it, because you cannot fix a search problem you cannot see, and this is the window into it.
Glossary entry