To cool by waving a fan or something similar. She fanned herself with a magazine to stay cool in the heat.
To spread out or move in a shape resembling a fan. The peacock fanned its tail feathers to impress the onlookers.
To stir up or intensify emotions or situations. His comments only served to fan the flames of the ongoing debate.
To blow air on something to make it burn more intensely. He fanned the embers to get the fire going again.