Webmastertools is a very convenient tool for site owners because it is a place where you can see how Google perceives your website and which changes should be in order. Its information which Google provides you with.
Usually Google informs web masters through an alert in Webmastertools. Now they will also start sending you e-mail alerts if something is up.
Types of alerts
In their blogpost Google explains there are two types of alerts: Site Error alerts and URL errors.
When you receive a site error alert it means something is up with your website in general, usually it means that Google cannot reach your site for whatever reason. In most cases this will be because the site has been down or firewalled or for example your robots.txt cannot be reached by Google.
URL errors focus more on specific pages of your website. This is based on an error message Google receives when crawling your website like a 404 error for example. These type of alerts happen more often and if Google would send messages to you every time that would in some cases almost be spam. So Google will only be sending you messages when they are seeing a big increase in these kind of errors.