When you cup the ball, you place your fingers further under the ball. So The fingers will stay in the ball longer and travel from further underneath the bowling ball.
The purpose of cupping the wrist during the swing is purely to shorten the length of the swing, increasing the rev rate to ball speed ratio. Today, with the high tech cores and coverstocks, cup is no longer necessary.
Also if you don't unload the wrist at the right time you risk injury to the wrist. If you watch the pros that cup the ball, they also uncup the ball at the release.
A more modern release would have more wrist cock entering the release and minimal wrist cup.
This eight minute video takes you from stance through release.
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