'Willpower' may be a vague term, but it describes a real issue. It describes the difficulty of people who have long term goals that get subsumed by short term urges.
We all have drives, say for example the drive to mate and the drive to eat, and these drives compete: can't mate if we don't stay thin, can't be thin if we eat those cookies. In the long term someone may want to lose weight, but the short term impulse to eat can override that goal, even if intellectually we know what we'd prefer. I suspect that human action is as much driven by our chemical drives as our intellectual choices.
Willpower refers to the ability to use the rational element of our psyche to repress the baser elements rather than having the baser elements override the rational. The more willpower someone has, the more he acts based on reason rather than instinct.
"What, you don't beat your children? What willpower!"
"You'd rather miss a meal than rob a bank? What willpower!"
"You don't murder your enemies? What willpower!"
Funny how easy life gets when you stop thinking about "willpower" and start doing the right thing.