Botnets

Botnet is a jargon term for a collection of software robots, or bots, which run autonomously. This can also refer to the network of computers using distributed computing software.


ShadowServer
While the term "botnet" can be used to refer to any group of bots, such as IRC bots, the word is generally used to refer to a collection of compromised, or Zombie computers running programs, usually referred to as worms, Trojan horses, or backdoors, under a common command and control infrastructure.

What actions are taken with these Botnets? 
Denial of Service Attacks, Spamming, Sniffing traffic, Keylogging, Spreading more malware,  just about anything malicious you can think of.

What can be done?
Running an up to date OS, anti-virus with the latest definitions along with a firewall is the first line of defense. User education and good computer usage is the second line of defense.

What about removal?
Removing these nasties from an already infected, compromised system should be left to professionals. You can't realize the extent of the damage with the current off the shelf consumer products. The correct tools, skill and knowledge are nessacary to successfully recover a compromised system and mitigate any damage that's already been done.