The swirled (helical) fletching makes the arrow spin in flight (sort of like rifling spins a bullet), which increases the arrow's stability, and at least in theory should result in better accuracy. Myself and just about every bowhunter I know prefer the helical fletching.
The only real problems with helical fletching are that it's harder to get complete rest clearance with the old prong style rests, and if you put too much helical on the arrow it will create a lot of drag and slow it down more as is heads downrange.