If you have ever opened your refrigerator door in bare feet you may have noticed cool air rushes out of the refrigerator across your feet. Cool air is relatively heavy while warm air is quite light.
Visualize what is happening when you open your refrigerator. Cool air spills out onto the floor like a blue river, while a red river of warm air is sucked into the top of your refrigerator.
Similarly, in the summer your air conditioner pumps out cool air which settles close to the floor. In the winter your heater puts out warm air which rises and collects near the ceiling, far from where you sit, sleep and work.
Since the warm air from your heater rises to the ceiling, your heater must run more often for you to feel warm. By reversing the direction of your ceiling fan you pull cool air up from the floor; that cool air mixes with the hot air near the ceiling and circulates down. This increases the efficiency of your heater, causes the room to be warmer and saves on your heating bill.
Operating your fan in the reverse position in the winter causes the fan to blow away from you, creating less draft. If you do not have a reverse switch on your fan you can turn it on in the low setting, while this is not as effective you will still gain some of the benefit of reduced heating costs.