A spambot is a computer that carries out the task of distributing spam, whether via E-Mail or Instant Messaging clients or otherwise. Spambots might also carry out other tasks such as mine valid e-mail addresses from a machine infected with malware, or even scan over entire websites for e-mail addresses that have been posted by users.
In most cases, Spambots are part of a network of other spambots generally referred to as a Botnet.