Fuzzy things are soft, downy, or furry. Few people can resist the charms of a tiny, fuzzy kitten.
Your dad's bearded face is fuzzy, and your favorite mohair sweater is also fuzzy. You can also use this adjective to mean "blurry" or "clouded," the way a badly lit scene in a movie might look fuzzy, with vague shapes moving in the dark. The inside of your head can feel fuzzy too, when you're groggy or dizzy: "I remember getting hit in the head by the soccer ball, but after that everything's fuzzy."