Wings produce lift because the air pressure is higher underneath than above the wing. Ever watch a plane landing on a very humid or foggy day and see the vapor trails curling from the wingtips? That is caused by air "spilling" around the tip of the wing from the higher pressure area below to the lower pressure area above the wing. The forward motion of the plane is what gives it that vortex effect.
Winglets decrease the amount of "spillage" of the high pressure air underneath. In effect (and vastly oversimplified), they trick the airflow into thinking the wing is longer than it is. "Spill" less of the higher pressure air under the wing and you don't have to produce as much to start with to get the desired lift. Producing that air pressure differential causes drag, so producing less causes less drag.
Jim