What is a botnet?

A botnet is where you send a trojan to someone and when they open it a "bot" joins your channel on IRC(secretly, they don't know this)Once done the computer is now refered to as a "zombie".
Depending on the source you used, the bot can do several things.
I myself have helped write one of the most advanced and secure bot sources out there.
(Off topic)

But once again depending on the source you can :
Keylog their computer, take picutes of their screen, turn on their webcam and take pics/movies, harvest cdkeys and game keys or even cracks, passwords, aim screen names, emails, you can also spam, flood, DDoS, ping, packet, yada yada, some have built in md5 crackers, and clone functions to spamm other irc channels and overrun a channel and even perform IRC "Takeovers".
Once again depending on the bot it may be able to kill other fellow competeter bots.
Or even kill AV/FW apon startup.
Add itself to registry.
Open sites.
Open commands.
Cmd,
notepad,
html,
Anything is possible !

Theres the infected computers "bots" the attacker, the server, and the victim