A fan cools you by moving the air around you. During the warmest weeks of the summer, it's easier to sleep if you have a fan in your bedroom.
Some fans are electric: you plug them in and a large blade turns fast and blows air around the room. Hand fans are small enough to hold, and as you wave them back and forth, they send puffs of air over your hot face. To do this is to fan yourself. A completely different fan is the one who follows a sports team or a rock band devotedly: "The fans jumped to their feet and cheered."