What is the force that moves the boat through the water?

It's lift. Like an airplane wing, a sail is an airfoil only vertical. As it passes through the air, the curved shape of the sail causes the air on the outside of the sail to go further and therefore, faster, than the air on the inside of the sail. According to Bernoulli's Principle, when the airflow increases, the pressure drops so the pressure on the underside of the airfoil becomes greater and "lifts" or pushes the sailboat along. See the link below for more information on Bernoulli's Principle.