Vane is usually short for “weathervane.” If the vane on top of the building is spinning, it must be windy outside.
In addition to being a device that shows you the direction of the wind, a vane can help direct flying things through the wind, as bird lovers and archers, among others, know. Be careful not to mistake vane for its homonyms, vein and vain. If you're so vain that you'll slash at your veins if the wind messes up your hair, check the vane before going out. Or just wear a hat.