I'm not an expert on this, but here is what I've learned:
First, these tapers reduce arrow weight without much loss in spine....which means a slightly faster arrow.
Bobtailed arrows have the weight forward which improves overall flight and allows for smaller fletches. It also reduces the "slap" (arrow rubbing against bow) that you hear when firing the arrow.
Chested arrows have less "wiggle" at the rear of the arrow when fired. This translates into less drag, and a little more speed.
Barrelled arrows have tapers at both ends and in addition to the benefits above, they are more forgiving if you have a shaft that is not perfectly straight. They also don't vibrate as much in flight as parallel shafts.
In general, tapers increase speed....which in turn creates a flatter trajectory...which makes it easier for some people to hit the target.
(sorry if this repeats some of what Pat said...he beat me to it.
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