1. Dementors suck the happy memories out and it's cold around them and if they get close enough they get your soul too. It takes happy thoughts to get rid of them, plus a spell that involves a white spirit of an animal, and once you've been around dementors the best therapy is chocolate.
2. Bogarts take the form of your greatest fear when you let them out of their dark hiding places. The spell to get rid of them includes laughter and the word spelled something like: Riddikulus.
3. Love and loyalty overcome darkness and evil. Over and again.
4. Being good to different kinds of people and personalities (elves, giants, spiders, goblins, centaurs) makes the world a better and fairer place.
5. Friendship and bravery are more important than knowledge and cleverness (that might even be a direct quote from book I). Goodness is better than greatness.
6. Spirits live on after death and watch and guide those still on earth.
7. Remorse puts a bad soul back together.
8. It's not what you're born, it's what you become. Our choices, rather than our abilities, show who we really are. (Also quoting here and there.)
There's more, and it's wrapped in the delightful series of Harry Potter adventures. I commend J.K. Rowling for doing what Brothers' Grimm and Disney did not do in their story telling -- for suggesting profound truths as she wove her tales.