If the wind blows against one side of the sail, then it pushes the boat downwind.
If the wind blows equally on both sides of the sail, you have a flag and the boat goes nowhere.
If the wind splits around the sail, the sail becomes curved like an airplane wing and areas of high and low pressure are created. The area of high pressure moves toward (pushes) the area of low pressure (pulls) and the boat moves forward. Simple.