Whimsy is what a person who's a dreamer and out of step with the real world might have lots of. People who are full of whimsy are odd, but often fanciful and lovely, like Harry Potter's friend Luna Lovegood.
Whimsy is also a whim — something you do just because you want to. If you find a postcard of Alaska and take that as a reason to move there, that could qualify as whimsy. Whimsy is irrational, but playful. If you decorate your house with whimsy, you may have a wall decorated with butterflies and giant daisies with googly eyes, and a couch trimmed with peacock feathers and vinyl. It's amusing and witty, and you’re a master of whimsy.