This tells you if Google has detected any malware on your site.
Any issues that Google encountered when as they were crawling your site are reported in this section. It a good section to keep an eye on. First tab is the HTTP errors and the date they were detected. The next tab is the pages that Google didn’t find, and then what is restricted by robots.txt, soft 404’s and lastly the unreachable. All these errors need to be checked into but keep in mind the date. You may have checked into an error in the last week but it can still show in the errors for awhile.
In the crawl stats section we get to see pretty graphs on how many pages google has crawled per day, the size (kilobytes) and the time it took.
Fetch as Googlebot
The fetch as Googlebot does just as it says. You type in the page you would like to check and will show you how the googlebot sees your site.
I think the HTML suggestions are one of the most useful sections as it tells you where Google has issues and where you can fix them. Google doesn’t like meta descriptions that are duplicated, too long, or too short but it will tell you if any of your pages fall into those categories.
Google also tells you if it had issues with your title tags. It will tell you if they were missing, duplicated, too long, too short or just non-informative.
You might also like to read :
Site Configuration - read what the site configuration section covers.
Your Site on the Web - read about the Your Site on the Web section.
Diagnostics - Read what’s in the diagnostic section.
Labs - Google playground.