A whirl is a quick spin, and when something whirls, it rotates fast. You can also use it to mean "a try." Hang-gliding? Snake-charming? "Sure," you say. "I'll give it a whirl."
Both whirl and spin are words that mean "turn in circles" but that have also come to mean trying something briefly––you might take a car for a spin or take a turn hiking in the Himalayas. All imply an attitude so free-wheeling, so easy, so devil-may-care that it might make your head spin. Or whirl.