I read a letter in Flyer magazine about winglets here is what it said, it is written in relation to GA aircraft but i think same concept of winglets is used on Jets.
Question: "Nowadays one sees more and more aircraft fitted with winglets. Some are small but others are several feet long. What aerodynamic effect do these winglets have?
Answer:
"The winglets fitted to aircraft have two functions. Their primary purpose is to reduce drag. There is lower pressure on the upper surface of the wing than there is on the underside - and as a result there is some span-wise flow towards outwards on the underside of the wing and inwards on the upper surface. When these two airflows meet they produce a vortex off the trailing edges and this is greatest at the wingtip: the air curls up from the underside producing a large vortex at the tip. This energy is all wasted, as it is almost all drag. Adding the winglets straightens out the airflow to a considerable degree and so reduces the aerodynamic drag a worthwhile amount in particular conditions - usually at cruise speeds. Some aircraft are fitted with fuel tanks at the tip, which have a very similar effect. In additional to the reduction of drag the winglets also produce a stabilising force in roll and so make the aircraft easier and more comfortable to fly - which is why some of them are so large."