Without getting too technical, those winglets were designed to reduce what is known as the 'tip loss factor'. That is a condition where the airflow at the wingtip of an airfoil circulates up and over the tip thereby impinging on, and creating a downward force on the upper surface of the wing near the tip, thus reducing lift in that area. Typically, the loss is up to about 3% of the total lift of the wing. The winglets prevent that by re-directing the downflow in a more horizontal direction, thus regaining the normally lost vertical lift at the wingtips. Quite simple actually.