This is what happens...take EliteFitness for example.
If you look at the topic page you can see that on an average day there are maybe 3500 people reading the various topics. All those people ask for new pages (discussion threads) maybe once every 15 seconds (that's purely hypothetical). The server computer can handle that kind of traffic without the slightest problem.
With a well planned DDOS attack, a script-kiddie (hacker) will try to gain control of hundreds or thousands of computers, and have them request pages (or some type of information) from a website server CONSTANTLY, over and over again.
So if someone can control 5000 computers, and have them request info from Elite 2x per second, that would be 10000 pages of information the servers would have to dish out every second, as opposed to 350 that they may get now. That much traffic could bring the server to its knees, effectively shutting the site down to normal traffic.
(The numbers were just for example, but the idea is the same)