This describes an Internet connected computer that has been hijacked by a Virus or Trojan infection. The computer can then be remotely controlled by a hacker, which means they can damage your system, steal your personal data, use the computer to attack other systems and or send out masses of junk email for abuse or personal financial gain. Multiple zombie computers are known as Botnets.
Related Articles:
> Computer Worm
> Trojan
> Virus