The expanded search information includes:
Diagnose potential problems that may impact your page ranking.
Which links from other sites link to your site
Top search queries that direct users to your site.
Suggestions for improving your site's HTML
Check to see if your site has been hacked
Firefox has a lot of addons that will help you with SEO, one of them is seoquake-seo-extension. this will give you a lot of information about a site which will appear in search results as shown below. If you go to a page the same results will appear at the top of your browser.
Both Alexa and Semrush provide free web analytics. All you need to do is go to either of their sites and type in the url for the page that you want to have analyzed. Both of these sites give some information that compares your rank and that of your competitors. Semrush allows limited views of the information after you have viewed a number of times you need to join and pay a fee.