DoS is a planned disruption of a website that is conducted by overloading a server with network traffic. There are different types of DoS, but basically they all overload the server by either tying up the computer's processing power or by filling up all the bandwidth available to the victim. In most cases, the victim's server attempts to respond to false requests and ties up precious system resources. No legitimate calls can get in when the system is busy acknowledging false requests. DoS can become a significant problem for individuals and businesses with a limited amount of bandwidth.
Zombies are essentially programs that can be set off by a timer or controlled by a master program.
The computers that are targeted for zombie placement are systems that are always live on the Internet. The zombies are timed to simultaneously send bogus data packets to the victim's server. All of this data, coming from hundreds of computers at once, blocks entry to legitimate users. It's like all Three Stooges trying to get through the door at once. There may be lots of jostling and squealing, but no one gets through until the pressure lets up.