A network created when bots are connected to eachother. Most commonly used for IRC bots such as Eggdrop, ComBot and Dancer. A botnet is used both by the bots themselves (to share their user files, request ops, etc.) and their users (as simple chat networks, distributed file repositories, etc.).
A more recent phenomenon is that of botnets running entirely on compromised computers typically used for the purpose of DDoS. These bots run specialized software which may not even be designed for use with IRC.