You can check search queries, internet and external links, clicks from search queries and many more, just type webmaster tools in google search and add your site and follow the procedure of verification.. Important: It will take up to 15 days to display data properly about your site..
First of all you should implement web-master code into your website design service or any of the other business website onto which you would like to have a look at. And after implementing that code and when ever you upload your site you may sign up at web master and after that by signing in you may look properly at your web-master.
I am trying to list out the functions.
1. Find search queries to do the SEO in better way
2. Latest links to your site to stay away from penalty
3. See message of manual actions if any taken by Google
4. Specify the target country for your website
5. For site crawl related information like crawl errors, stats, Robots.txt, sitemap submit and for advance SEO URL parameters
6. Fetch as Google bot to check how google bot see your webpages
These are the basic functions. Apart from this you can use it for microdata if you are not able to add it through coding.
Attention: "role based name" email prefixes such as support, webmaster, info, contact, forum, service, affiliate, admin, traffic, partners, marketing, etc., for our member accounts are not permitted. They are acceptable for a vendor listing, but not for the member email. This is due to bulk email processors scrubbing them for delivery due to extremely high bounce rates. Please apply for membership using a personalized email prefix. Something like email@example.com.
If we discover you signed up with a role based name we will give you only one message to change it. After 3 days your account will be removed if the email is not changed.