The denial of service is achieved by individual computers flooding a network or webserver with so many useless requests (traffic) that it can no longer cope and therefore fails to handle the requests.
This prevents everyone from accessing the websites or services stored upon it.
The useless traffic flooding the server is often caused by many compromised systems (a botnet) under the control of the attacker. This is known as a distributed attack (DDOS).
DOS attacks are usually temporary but can be very damaging during that time.
Victims can range from large companies through to individuals.
Although large companies are a bigger target, they are also often best placed to deal with such an attack.