Unicast is sending messages to a single peer. Broadcast is sending messages to everybody. Multicast is in between, sending to some arbitrary set of recipients.
On a Local network, multicast is very easy to do. Unless it's very, very old your computer almost certainly uses multicast on local networks already, for a variety of purposes. A dumb old network just sent all packets to all computers on the local network, so both broadcast and multicast were equally easy to do, your network card has a filter built into it, that autonomously weeds out messages your computer cares about, and ignores the others - so the Operating system is like "Hey, network card, my unicast address is 10.20.30.40, and I am also listening to multicast address 224.0.0.251" and it will just throw away any packets that aren't for those addresses. A smart modern network (e.g. the mid-range gigabit switch serving your desk at work) keeps track of which addresses are where and sends copies of messages only to where they seem useful, leaving more network bandwidth for everybody else.
The Internet can in theory do Multicast too. I've used this to, for example, watch television with a dozen other people without any copy of the TV picture data being sent over the shared data link to us more than once. That's what those addresses are for, you "Join" one of the multicast addresses and begin receiving, say, the Olympics live.
However making all this work is hard, and in most places, most of the time, nobody puts in all that hard work, so probably you'll find that although local network multicast works for you (as I said it's used in modern systems) you cannot use the Internet's multicast features. Which is a shame, but we can't have nice things.