Well, that's what the media are claiming. Members of the hacktivist collective, known as Anonymous, will shut down the Internet this Saturday, in Operation Global Blackout, by attacking the Domain Name Servers (DNS) servers that run the Internet. When you type www.anyname.com into your browser the DNS servers translate this into an numeric IP address, like 192.168.1.103, which is the actual physical address of the web server you want to reach. Every computer on the Internet has an IP address, including the one you are reading this on. But, you'd struggle to remember these numbers, so the DNS servers translate, from easy to remember domain names, to hard to remember IP addresses. For example, www.google.com is actually, 22.214.171.124.
DNS servers are organized into a hierarchy. At the top there are 13 root servers. These contain the master database of all the world's IP addresses and domain names. Below these are tiers of increasingly more local DNS servers that contain copies of the root server databases, right down to DNS servers in you local ISP, to which your computer is connected. Anonymous will not be targeting the root servers, these are very secure, but will be attempting to take down DNS servers in local ISPs and regional telcos that control the backbone of the Internet. Will they succeed? A professional computer security friend of mine says, "...they will be at least partially successfully. Lots of old unpatched top level DNS servers out there."
You can learn more about the shadowy world of hackers in chapter 12 "Digital Underworld" of The Universal Machine.