The denial of service is achieved by flooding a network or server with so much useless traffic that it can no longer cope, preventing 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.
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.