A way of interconnecting equipment so that a default signal routing scheme can be set up, but flexibility is preserved allowing reconfiguration of all gear interconnect at any moment.
More succinctly: it's a way of getting all the input and outputs into one central location so that you don't have to crawl around on hands and knees behind your mixer, multitrack , or outboard gear rack every time you need to connect two thinguses together.
This would be a good time to try out the "search" function in the upper right hand corner: try searching on the keywords "patchbay" and "normal", and you'll see a large amount of discussion that has already been done...