While Google Analtyics is one of the most widely used SEO, Search Engine Optimization tools, Google Webmaster Tools is a hidden gem that can be used to increase your web presence. It uses information from indexed keywords, meta tags, internal and external links, and other Google trickery to analyze your web page.
Diagnostics: This section is broken down into 3 parts to describe each of the major crawls. Web crawl deals with errors that standard browsers would acknowledge. Mobile crawl deals with errors that mobile and slimmed down browsers would acknowledge. The content analysis feature will alert you of duplication errors, broken links, length restrictions, and non-indexible content issues.
Statistics. Being the most useful feature list of this tool, you can find Top Search Queries, Crawl Stats, Subscriber Stats, Googlebot Stats, and Index Stats. Googlebot stats include words and phrases containd in inbound links to your website.
Links. View your pages with internal and external links. This is great if you are not the only content provider for your site. The site links page is useful for larger sites to see what their Google search answer will look like when a user searches for a specific string.
Tools. There is also a robots.txt manager, 404 page manager, a iGoogle widget, and a Google Sitemap Generator available for your use.
Take the Tour of Google Webmaster Tools here