An engine is an air pump. It sucks air (and atomized fuel) in by creating a vacuum when the piston goes down with the intake valve open and pushing air (and gaseous products of combustion) out when the piston goes up with the exhaust valve open.
Just like with a vacuum cleaner, when you put an obstruction in the way (your hand) the engine can't suck as much air when there's a restrictive air filter and a small hole in the air box that allows limited air in.
Similarly, if you restrict the exhaust it restricts the intake of air, because less out means less can come in.
So the short answer is whenever one allows more air in, more fuel must be made available to keep the mixture in the correct proportions of air to fuel. One does this by allowing more fuel to mix from the carb. A carb has got three circuits that all interact to provide the proper mix. They are the idle jet, the needle and the main jet.
In rejetting the idle jet is seldom replaced, but the screw that adjusts flow is usually turned out to provide richer idle (and up to something like 30% engine speed). The needle (which is simply a needle of exacting profile suspended into the main jet) is either adjusted up to richen, or replaced with one having a more appropriate profile. And the main jet, which only directly affects wide open throttle (WOT) is replaced by one with a larger hole.
Getting thos all balanced right can only really be done on a dynamometer or by doing chop inspections of the spark plugs. However Dynojet and other companies have put together kits of stuff that have been developed on various engines that can get pretty close. Unfortunately, they tend to err toward the rich to avoid erring lean and damaging engines. But they make a good starting point.
The long answer is rather more involved because the real intake dynamics have more to do with relative pressures than actual amount (mass) of air coming in. And exhaust isn't nearly as much of an issue as intake, despite what the marketeers will have you believe.
In any case, bikes are sold in a very lean condition, so even without opening intake and exhaust, rejetting is valuable to get better power, smoother transitions across the rpm range and lower operating temperatures. Think of it as putting the bike back together as the designers intended, rather than as the government mandates. (Airboxes, restrictive exhaust, various emissions stuff all fall in this category.)
Your dealer can make small adjustments to the mixture using their Mathesis Tester. Commonly referred to as 'adjusting the trim'.
This can improve the part throttle performance, making it more user friendly in traffic, run smoother at low rpm, etc.
There are several aftermarket parts that allow you to change the mixture over a wider range. TechLusion (?), DynoJet PCIII and the FIM Ultimap are ones I know of.
I'm using the PCIII, and had it dyno-tuned. Substantial improvement in user-friendliness. Got a little more HP too.
Re jetting is basically replacing the jets (fuel sprayers) with more open jets, there fore allowing more fuel to be burnt to make more power, of course if you have more fuel you need more air.
Don, I disagree with you about dynojets kits, I put their stage II kit on my mikuni's and used the 38 jet, I followed their instructions by turning the mixture screw 2 and a half times and my fuel air mixture came out perfect.