Botnet is a jargon term for a collection of software robots, or bots, which run autonomously.
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 machines running programs (usually referred to as worms, Trojan horses, or backdoors) under a common command and control infrastructure, often called a zombie master.
A botnet's originator, or master, can control the group remotely, usually through a means such as IRC, and usually for nefarious purposes. Individual programs manifest as IRC "bots". Often the command and control takes place via an IRC server or a specific channel on a public IRC network.