Search Console is a tool that shows which search queries a website appears for in search results, how many times, with what average position, and with what click-through rate. It is the only source of actual queries from users, and therefore has greater value than estimates from third-party tools. In practice it is used for three things: finding pages with a high number of impressions and a low click-through rate, where adjusting the title and description helps; discovering queries for which the site appears incidentally and which would deserve their own page; and tracking the impact of changes by comparing periods. The data is sampled and filtered, so it need not match analytics. The tool also reports technical indexing problems. In addition, the data is retained only for a limited period, so it is worth exporting it regularly and keeping your own history.
Source: developers.google.com
See also: Index coverage report, Click-through rate optimisation, Keyword mapping to pages.
