A patchbay is simply a way to route signals to different pieces of hardware, without having to plug and unplug those devices devices directly. It saves time, keeps things more orgainized, and make routing easier.
Let's say you have a compressor, an EQ, and a DeEsser, and you need to record or mix a vocal.
The compressor, EQ and DeEsser are already hooked into the back of the patchbay, and you have the ins and outs marked on the front. You can now decide what route you want that vocal to take, just by choosing which processor you want it to go through, and in what order. Say you want to compress first, then EQ, and top it off with a bit of deEssing. The output of your vocal would go to the compressor 'in', the compressor 'out' then goes to the EQ 'in', the EQ 'out' goes to the DeEsser 'in', the DeEsser 'out' goes back to where your vocal is being recorded or mixed. If you wanted to change that order, it would be as simple as just reordering the patch points.
Make sense?
...I don't even want to imagine the more complicated stuff I haven't even touched on yet...whew....