Broadband is actually a kind of broad term. It's often explained using a hose or pipe analogy - e.g. broadband is like a firehose, as opposed to the garden hose you're using now. However, confusingly, it doesn't simply refer to one particular technology, some special wire with enormous capacity.
What the different broadband delivery systems have in common is that they use digital technology to compress enormous amounts of data - be that video, voice or printed material - and get them through to the consumer many times faster than even an ISDN line, of the sort schools have acquired in recent years. Broadband doesn't make it possible to download movies, games and other large files - that's been possible for a long time - but it does make it practical, thanks to its speed.
That speed isn't a matter of hype: a 1.5 megabyte file might take three and half minutes to deliver via a typical 56k modem; your school's ISDN line is more than twice as fast: 90 seconds. But even a relatively slow form of broadband, the assymetric digital subscriber line (ADSL) that runs through a phone line, can do it in under 25 seconds. And the connection can stay on all the time without interfering with your telephone use.
Broadband can run through the cables that delivers TV to many homes. You can also get broadband through "fixed-wireless" systems, which send data from antenna to antenna, or via satellite.
Companies such as Sky, which deliver TV stations via satellite direct to users, can also deliver Internet access. Other companies are promising to focus on satellite Internet connections. Like some other broadband systems, satellite connections are much more speedy at receiving than for sending data.
The broadband network, of the sort the Government is talking about for the west coast, offers an amazingly high-speed, high-volume connection. It won't run directly into your home, but it will make Internet information move a lot faster to your PC.
In summary, broadband promises an end to the "world wide wait"; more reliability; far better "streaming media", especially video; increased ability to share software over network. What the technology can't promise is that there will be anything worth using on these systems.