In winter, slow-turning ceiling fans push warm air back down to the living spaces. In summer, ceiling fans, on any speed, pull warm air up and away from living spaces, while also creating a breeze.
During the heat of summer, ceiling fans should rotate counterclockwise. The blades, due to their slant, push heat down and around, creating a "wind-chill effect," noted the Energy Star website. Your room will feel cooler.
In winter, the ceiling fan blades should turn clockwise, gently pulling the air up to recirculate it down toward the living space.