To be perfectly honest, I'm sure that I'll miss a few points in this section. Botnets can do a lot of things and I'm sure a few more inventive ideas will come around shortly after publishing this. Since a botnet is just a mass of controlled computers, the options are effectively infinite. A few common uses stand out though.
Probably the largest known use of botnets is for spam emails. Most major spam operators use ridiculously high amounts of bandwidth. All those little emails add up really fast. Spam emails are also frowned upon by just about everyone, so once again, spammers prefer to use someone else's computers. One very famous network is the Storm Work Botnet. This botnet is believed to have millions of computers under its control that all send out spam to inboxes around the world.
Another possible and popular option is to build up a botnet to allow for successful DoS attacks. Denial of Service attacks aren't complicated. It's a fairly simple way of overloading a website and making the server shut down. For another analogy, just imagine that you and a few thousand friends all rush into a deli and start shouting orders. Of course they can't handle any one order, so a jam forms and continues to build. It won't take long until the shop just shuts down until they can figure out just what's going on. Having a botnet on hand allows a cyber criminal to send out large numbers of simultaneous results to a website to waste it's bandwidth and shut it down. For another example, we can return to the Storm Network's activities. As discussed here, the botnet carried out DoS attacks on an antivirus website as a means of self preservation. The sites were able to stay online, but they had to dedicate staff, software and hardware to defending themselves. Since the attack was basically free for the assembled botnet, it was a good way to harm an enemy.
General scamming also puts botnets to use. Remember that having a bot on hand allows them to make use of someone else's computer. While they wouldn't really need a network for this task, being able to use an apparently unrelated machine would certainly come in handy. Naturally there are creative variants. It was suspected that an early use for Storm was to send out "stock tips" to artificially inflate a stock's price so that they could make a quick buck before the bubble burst.
Of course, there are other creative uses. I have heard rumors of people using botnets to stealthily (or so they think) click the ads on their own webpages to defraud advertisers and Google. Some botnets are supposedly used for private piracy networks. If the master has the appropriate script for his botnet, then they should be able to create fake accounts on facebook and myspace for phishing activities.
These are just some of the options of course. Now that you understand just what a botnet can do, check the next page for how to keep your computer safe.