After winning a fight in the game you are shown a summary of units and their post-combat condition, as well as the reward.
One reward I have seen so far is money, "Gildar", that's easy enough, but what does "Gildar Ability Point" mean? Is that experience for the heroes? I haven't seen the current XP amount go up by the amount listed when I choose the Ability point option and comparing to a save file, so what does it actually do?