A botnet is a group of Bot infected PCs that are all controlled by the same "command and control centre". Recently peer-to-peer (P2P) botnets have been used. These botnets do not have a traditional command and control centre but they are all part of the same "army".
BotNet’s can be used for a myriad of tasks, the most common of which are sending masses of spam email and participating in distributed denial-of-service attacks (DDoS). Often users are completely unaware of infection by design and might not even notice infection as the bot uses a small amount of processing or network power. But once you add up every bot in the botnet, they can be extremely powerful.