A robot network or botnet is simply a cluster of computers running a special application that's maintained and operated by the owner or software source. To be more specific, a botnet either refers to a legal, legitimate computer network that share program processing among individual units or illegal, malicious ones used to perpetrate cyber crime, the spread of malware contagions, DOS or DDOS attacks, and other hacker-related activities.
The illegal kind of botnet mostly refers to a group of computers
Contaminated with a viral or malicious type of robot software (the bots) and is usually spread via the Internet or network connections. These bots present a significant security hazard to your computer, especially once the bot (known in general as malicious software or malware) has successfully taken over your machine. Your computer basically becomes a "drone" or "zombie" of sorts that's unable to oppose the manipulations of the bot commander or hacker once it's part of a botnet.
Depending on the overall sophistication and complexity of the robots used, a botnet could be large- or small-scale in terms of volume. A particularly humongous botnet may have over ten thousand individual infected zombie computers at the very least. As for a smaller botnet, it's usually made up of about a thousand drones or less, which demonstrates that even a considerably minor contagion is still quite formidable in terms of numbers (although it cannot be compared to the truly gigantic, corporation-destroying botnets).
More often than not, the owners of compromised machines are none the wiser in regards to their dire circumstances, so they're blissfully unaware of the fact that their computer's resources are being manhandled and abused remotely by a person or group of hackers through the IRC (Internet Relay Chat).
At any rate, there are many types of malware bots that have already spread (and are continuously spreading) across the worldwide web. There are also bots sporting scripts that allow them to contaminate other computers at will (also known as spreaders), which has forced IT security experts to categorize these threats as computer viruses in certain scenarios. Then again, there are other types of botnets that completely lack such advanced, system-crippling features.