Phrase implies a significant and positive change in someone's condition or mood. The good news from home will do him a power of good.
Pro Tip 2/3
Colloquial Use
Used in informal conversations among friends or family, not in formal writing or speeches. You look stressed; some time off would do you a power of good.
Pro Tip 3/3
Emotional Support
Often refers to emotional or psychological benefit, not just physical. Talking to a counselor will do her a power of good.