If something is woolly, it's covered in (or made of) soft, curly fur. Don't forget to wear your woolly hat — it's cold out there!
You can use this adjective for anything made from wool, like your favorite woolly sweater or the woolly socks your grandma knits. It's also useful for things that look or feel like a sheep's woolly coat: "Look at those strange, woolly clouds!" "He shaved his woolly beard off!" Informally, it can be a great way to describe confusion or befuddlement, like the woolly thoughts that go through your mind when you're absolutely exhausted.