At its most basic, the Shoutcast system is based around a 'client + server' configuration which allows you to run a server (either directly or via a hosted service) which can then provide a stream or streams of the 'source' connected to the server to any clients which are connected to the server.
The clients connect via a direct connection i.e. server <->> client where the main flow of data (the stream data) will go from the server to the client.
So a simple SHOUTcast setup would consist of the following:
Winamp + DSP > DNAS [sc_serv] > Winamp (Source) (Server) (Client)
This is not the only way to setup a SHOUTcast system and more examples can be seen in the shoutcast_system_overview which goes into more detail about the way SHOUTcast works as well as other ways of setting up a SHOUTcast system (see Wiki section 2.0).