Google Search Console, previously known as Google Webmaster Tools is a close cousin of Google Analytics but fulfils a rather different function.
A simple way to describe the difference is this: Search Console provides an information on how search engines interact with your site, while Google Analytics provides an information on how website users interact with your site.
Search Console is primarily about monitoring the results of your SEO, so that you can see how successful your efforts have been. For example, you can tell where each of your web pages or blog posts rank for a range of key phrases.
It gives a great wealth of information and to the trained eye can also suggest ways in which a webpage may be further optimised. One fantastic advantage that Search Console has over other ranking tools is that you do not have to enter a set of key phrases yourself, in order to find out where they rank. If a phrase ranks anywhere, even if it is only placed at no 87, it will be listed.
Search Console is also the vehicle via which you submit an XML style sitemap to Google. This tells the search engine about all the posts, pages and images on your site, where they exist and how they are related to one another. Although these days, in theory at least, you don’t absolutely have to submit your site to Google. In my experience at least it speeds up the ranking process. It’s also a great way to get new and important site content listed.