unicast is just like it sounds, one cast, you send a packet addressed to a specific person, anywhere in the world, like a cell phone call.
broadcast is more like a radio station, you send out a open ended signal to everyone in your area, with limited range.
multicast is a hybred of the two, like a conference call, you talk to a bunch of people, anywhere in the world, and you old have to talk into one phone to do it.
multicast and broadcast are really one way, the "client" has to send back a unicast transmission to give feedback to the server, though they can broadcast or multicast of themselves to the whole audiance.
it get's a bit greyer at the network level, but suffice it to say that most normal communication is unicast, most of the network cogs and wheels (that you never see) are broadcast, and most of the pull-feed stuff, like streaming media, are multicast.