A botnet is a collection of PCs that have been hijacked by virus and worm attacks. Sometimes these attacks are as innocuous as opening an malicious image file on an unpatched system. The image load causes a buffer overrun executing a binary payload. The payload causes the system to connect to a server reporting it's state and then it goes dormant until a remote attacker initiates programs on the server.
Once a PC is so infected, it can be used in tandem with similarly-infected PCs to send spam, post to blogs (comment spam), participate in denial-of-service (DDoS) attacks or worse.
eWeek goes into great detail with a few interesting scenarios in: "Is the Botnet Battle Already Lost?"
Patch your systems folks. Windows users can visit http://update.microsoft.com/ on patch days and use OneCare for all-in-one PC protection.