Distributed Denial of Service (see DoS).
A distributed denial of service is many computers on the Internet coordinating a Denial of Service attack (DoS) against a single host, network or network infrastructure. A DDoS doesn't need to fully exhaust your services, but merely keep a steady monetary burden on the current state of your service, forcing you to eventually give in and stop the service altogether.
A DDoS can be performed by people who have hijacked a great number of hosts to do their bidding (these are known as "zombie hosts"). A target of a DDoS is usually chosen for one of several reasons. Frequently, the attackers are after some form of financial gain, usually in the form of extorsion (e.g. "Give me $1,000,000 or I will continue the DDoS until you go out of business."). Sometimes the attacks are launched due to moral, political, or religious objections to the owners of the target systems.
Stories posted to various other high-profile websites can be seen as a limited form of a DDoS. When a URL is posted, the (many) thousands of readers click on the link within in short period of time. The huge number of requests will frequently overload the remote webserver with the added load. One of the first sites to contribute to phenomenon was [Slashdot], and when a web server is unable to handle the incoming HTTP requests, it is said to have been "slashdotted." This drives home the point that freedom of speech on the Internet can be a costly affair. While this can be destructive, a typcial "slashdotting" will only last a day or two; once the story containing the URL is removed from the front page of the news site (such as Slashdot), the number redirected hits drops off tremendously.