A friend of mine asked why some airplanes have winglets yesterday. The Wikipedia article has a fine explanation, but I thought I'd try my hand at explaining a part of my field you're more likely to encounter in your daily life than, say, bell nozzles.
The wing's main purpose in life is to produce a pressure difference between the top and bottom surfaces. The contours of the wing force air to accelerate over the top surface, dropping pressure relative to the bottom, and providing a net upward force on the airplane, allowing it to fly.
At the wingtips, though, this pressure difference can't be maintained. High-pressure air on the bottom spills over to the top surface, swirling around in a horizontal vortex at each wingtip. The vortex influences the air travelling over to the wing, pushing it down, making the wing feel like it's canted downward into the oncoming flow. Since wings produce more lift the higher they're angled into the oncoming airflow, this reduces the lift on the wing, while the friction drag of air grinding over the wing remains the same. To cruise the farthest while burning the least fuel, maximizing the amount of lift per unit drag is crucial, and any innovation that can improve wing lift without increasing drag is one of the sweetest prizes an airplane designer can win.
Suppose that the tip of the wing curved up for the last few feet instead. There would still be some pressure difference between the outboard and inboard sides of the wingtip (or winglet), but since the vertical section itself isn't producing lift, it would be less than in the winglet-free case. Wingtip vorticies are less intense and further away from the main, lifting, section of the wing when winglets are present, boosting wing lift and allowing an airplane to carry more payload further for the same size wings.
To pay for this cruise lift-to-drag coup, the airplane now has to carry two surfaces that weigh something and add some skin friction drag. The optimum size winglet is that which properly balances the drag reduction from moving tip vorticies away from the wings with the drag increase from the extra surface area and the fuel penalty of lugging an extra few pounds to cruise altitude. For small, short range aircraft, the optimum winglet might be none at all, though the Rutan Long-EZ proved the concept on a small scale in the early 1980s. Typically, the longer the airplane's mission, the more sense winglets make.
It's hard to comprehend the violence of what air can do at high speeds, given how docile it is in our everyday experiences. Even at "low" speed, while descending to land, air hits the wings, tail, and fuselage with the force of a hurricane. The next time you're flying to or from a humid place in the summer (say, Houston or Orlando), take a look at the wing on your way up or down. Vortices at the tips and gaps in the wings churn the air so hard the water condenses into a wispy filament of cloud, a tornado's funnel cloud in miniature, but with the majesty preserved. That's the airplane, holding you and a hundred strangers high above where you began. It's an impressive sight.
