Willpower refers to that line of white bars across the top of the screen. I've noticed that when you accumulate enough of those, your energy level will max for awhile, allowing you to boost your stats quite a bit during the day. Keep an eye on it though, because when you run into one of the bosses and your willpower is next to nothing, she will beat you right down and it will take a LONG time to build it back up again.
Just remember to go dancing every morning and take a shower too, to get an extra energy bar. The shower will show up after day 20. One of the girls from the 'Asylum' game will wake you up when it's open.