http://en.wikipedia.org/wiki/Winglets

Basically they improve fuel effeciency.  The longer a wing is the more lift it generates, or in other words, the more surface area there is the more lift.   However more surface area means more drag, so there is a tradeoff.  With a winglet you effectively increase the surface area (although not the extent of just lengthining the wing) but you create less drag than you would if you lengthened the wing.  They also reduce wingtip vortices that can cause drag.  Also, they look kinda cool, but that's not why they are there.

Without going into long drawn out explainations...

Whenever a wing generates lift there is a high pressure area below the wing and a low pressure area above the wing... during these two pressure systems attempt to equalize with one another the wing is pushed upward creating "lift".

BUT at the wing tip this high pressure air below the wing is able to actually reach the low pressure air by "spilling" from the bottom to the top of the wing, this creates a vortex of spiraling air sort of like a horizontal tornado that trails behind the wingtips for quite a distance - a few miles in some cases. this is called "wingtip vortices" or "wake turbulence". these cause large amounts of induced drag, and are an invisible hazard to any aircraft that may be flying behind the generating aircraft.

Winglets are placed on aircraft so that the amount of air that causes the wingtip vortices to occur is greatly reduced, because it creates a barrier preventing the unwanted airflow and reduces the flow of air from bottom to top of the wings at the tips.

because of this reduction to the wingtip vortices drag is reduced, fuel burn is reduced, and hazard to following aircraft is reduced making winglet equipped aircraft more efficient.

From what I've heard, there's a couple of roles they fulfill. For all I know, there's more.

I think they serve to improve stability, and I know that the winglets on some airliners - like the A380 - are designed to reduce wake vortex.