The simplest way to think of it is a central point where everything can be plugged-in and routed via patch cables wherever you need the signal. It can save you a lot of bumps on the head climbing behind your gear. If you find yourself hooking up and/or moving cables a lot, you'll probably thank yourself after getting a decent patch-bay.
Got CD inputs/outputs? Cassette(s)? DAT? Soundcard? Mixer, preamps, effects, kitchen sink? Hook 'em all up to the patch bay and connect 'em where you need 'em. If I want to hear a cassette, I can "patch" the cassette outs to two channels (stereo) on my mixer in seconds with a couple of cables. Or to the inputs of my DAT. Or anything else that's hooked to the patch-bay and accepts the same input level.
It's a bit more involved than that with balanced/unbalanced, normaled and half-normaled inputs, and a few other odds and ends.. but you get the basic idea.
You're also adding a little more cable length, more connectors to make good contact, and generally more places to check for failure. It's not a huge downside, since you can always bypass the patch-bay if a situation becomes that important. Also, be sure to save a good chunk of your budget for cables if you decide to get one (or twenty). Everyone, including me, seems to overlook that part when shopping for patch-bays.
