Network traffic is sent in packets, each containing a certain number of bytes.

A Denial Of Service (DoS) attack works by flooding a server or service with hundreds/thousands/millions/etc. of requests at once. Sometimes those are meaningful requests, like lots of HTTP requests; sometimes they are just random packets of crap. The result is often the same: the end server's bandwidth is clogged up with the DOS attack rather than 'real' requests.

Problem with a DOS is that the computer sending it needs an equal amount of bandwidth and resources to make the attack. If you want to flood a server with 1.5GB/s to knock it offline, you also need a 1.5GB/s pipe your end. Most [all] people don't have that.

The solution is rather than having a single computer launch the attack, you split it across multiple computers ... you "distribute" it, hence Distributed Denial of Service (DDoS). Each computer launches a little part of the attack, and collectively they flood the destination server. So instead of 1 fat computer with 1.5GB/s bandwidth needed, you can have 1000 computers each with 1.5MB/s bandwidth (which is realistic). It also makes it harder to block, as you can firewall a single computer, but firewalling 1000 computers is harder.

This is what a botnet is usually used for. The 'bots' in the botnet are all told "go start doing a little DoS attack against this server", and suddenly you get a huge DDoS attack against that server. Some botnets have only 10 or so clients; others have millions. BredoLab is listed on Wikipedia has having over 30 million bot clients...