simply botnet is an irc client holds many features ( scan , download , ddos , ftp server , sniffer , ... etc)
when we say its an irc client this doesn't mean its normal client like ( mIRC , xchat )
its hidden irc client that work in background
the reason for connecting simply is to control the botnets actions
for sure its a considered as a virus .
answering your question : when you have a big number of infected computers ( botnets)
simply you can order a big number of computers ( 50 or 100 k) to start packeting the target (website/server) and this what we can call a ddos
i forget to say its illegal to collect bots ... doing this you maybe arrested