The first answer is a good high level answer.
The idea is basically that instead of a single source device sending out 100s to 1000s to millions of streams of the same content. The source sends out one stream of content and down stream devices (routers) replicate the stream and forward out, but only to those devices that subscribe to it. The source can function more efficiently this way and it reduces the burden on the network.
Common applications for multicasting are distance learning (i.e. virtual classroom), real time stock tickers, real time news feeds where the info is pushed to you instead of you going to get it. Stock exchanges are big users of multicast protocols. NASA uses multicast protocols for space flight telemetry.
Look up PIM-SM, PIM-SSM, IGMP(current version is V3, as in IGMPv3) on google for the details. Multicast uses specific IP addresses.