Attacking/using moves

Is there a relation between the attack icon and how to make the attack/move more powerful such as swiping the screen as it looks to show because it never seems to work for me. Any help is appreciated.

The icon for the move just shows you how to swipe such that you use the move. For example, if you use timestrike by swiping right over an Omegawyrm, then you will use timestrike on the Omegawyrm. The power is not dependent upon swiping whatsoever.