If apps use it, it can be very good.
Though it's not integrated well in Windows (given it's Apple's stuff, not Microsoft's). But in Mac OS X it's excellent.
If you want to connect to a printer or another computer on a network, you usually need to know its IP address (something like 192.168.1.6). This isn't very natural for humans, so Apple made it easier.
Devices with Bonjour support send out their name on the network. So they say "hey, I'm Claire's computer". This means that on your ccomputer, you can simply choose this name, instead of having to type an annoying IP address.
(It was originally called Rendezvous, but there was some trademark issue. There's an open source free alternative called Zero Conf for GNU/Linux systems, etc.)