Google alerts are automatic email alerts of latest and relevant search results sent to your inbox by none other than Google itself . Google search engine crawlers continuously crawl content from sources such as news , blogs , web , videos , groups etc and when they find anything that mathces your defined-alert criteria , they will send you can email alert with a link to that page that contains your search term .
See the following image . It is Google alert for the search term “http://onlineearningguide.blogspot.com“ . I have set the alert for my blog previous URL ( you can feed in any term you want , just consider this as an advanced search query for which the result will be emailed to you ) . When Google found new pages that contained my search term , they sent me the following email along with the link to the page containg my search term .
Lets keep it simple If you want to track whose talking about you on blogs, groups etc then you can set an alert of your name as search term and if some one uses your name and google catches that , they will send you and alert immediately ( depends upon your alert settings ) . By using Google alerts you can keep track of latest stories , news and can even keep an eye on your competitor . It is entirely up to you 
You can set up as many as 1000 alerts per email address (only Gmail address accepted) .