Power Up Points replaces the REP stat for enemy units in the Yggdra Union series. Its main function is to determine how much power a card gains when that unit is defeated. Boss units like Leon will have higher Pow. Up Pts than their grunts.
The amount of Pow. Up Pts awarded to a Battle Card is proportionate to the amount of morale damage the unit took in battle. The amount is subtracted from the total Pts the unit has, which leaves the unit with whatever remains after the clash has ended. If the unit is killed, then all remaining Pow. Up Pts will be allocated to the card that was used.