UA100 responds:
Unfortunately, the answers are almost as broad as are the questions in this one. "Quite simply, a jig is anything used to make repetitive parts. Typically a jig guides a router bit through a specific, repeatable cutting action, allowing you to make identical pieces." Jigs may or may not make reproduction of identical parts possible. They do make repetitive identical cuts possible, but there is no need for the cuts to form "parts." A good example for my point is a dado jig for a router. Hell, even a rabbeting bit is a jig all on its own. It forms ledges on parts, not parts. THe rabbeting ledge on a jointer might be considered a jig, as well.
Typically, a jig can be used with almost any tool, not just a router. Anyone with a jig for their tabllesaw, raise your hand. For your dirll press? For your shaper? For your bandsaw?
The original question should have been reduced in scope, giving it some focus, and then an answer would have been possible, and easier to make clear.
Charlie Self "In our civilization, and under our republican form of government, intelligence is so highly honored that it is rewarded by exemption from the cares of office." Ambrose Bierce