I see that some smartphones now have dual LED flash.
What exactly is the purpose of a dual LED flash? Anything to do with brightness? What can a dual do that a single flash cannot? Would a triple LED flash be a possibility even?
The distance from which you can light subjects with a flash is proportional to square root of luminous power due to the inverse square law. A dual LED flash can emit twice as much light as a single LED, which means you can lit subjects 1.4 times further away. It also draws twice as much power.
A triple LED flash would increase your reach 1.7 times compared to a single LED (1.2 times compared to dual LED). So the difference is not as significant as when stepping from single to dual, but increase of manufacturing costs and power drain is similar. Triple LED flash is not unheard of - Pentax Optio W90 uses three LEDs to aid during macro shots. As they are placed triangularly around the lens, they effectively create a ring light effect.
Generally, if you need more light than a dual flash, you'll be happier with a Xenon flash. A Xenon flash would also let you add regular speedlights off-camera in optical slave mode, but cannot act as a continuous video light / torch.
In iPhone 5s (and hopefully, its successors) the two LEDs are of different color (amber and white). By adjusting their ratio, the camera can adjust color of the flash to match what been determined to be the white balance of ambient light. Traditionally, photographers have had to use gels to obtain similar match between flash and ambient light.
Such color adjustment is intended to reduce washed out look of flash photographs. There are actually two factors contributing to the washed out look - mismatched white balance and on-camera axis of the light. Dual flash fixes only the first of them; axis still remains unnatural for those of us who don't walk around daily with a head lamp (unlike miners). The axis could be fixed by bouncing the flash from a nearby surface, but this is where illumination power falls short for even a dual LED flash, even if there was a reasonable way to direct the light.
Greater illumination. Three LEDs should be brighter, although would use more power.
Here are some example pictures comparing images produced by several Nokia mobile phones equipped with single LED, dual LED, and Xenon flashes.
Another possible use of a double-led flash is to fiddle with the light color temperature. There is an implementation in the dual LED flash in the iPhone 5S.
The idea is having two sources of light with different color temperatures (say, daylight and a reddish one) and to balance them to have a more natural "fit" with the ambient color temperature when using the flash as a fill-in or as a secondary source.
You can use the same mechanism used for calculating the automatic white balance and then combine the two light sources to have something that approximate the color temperature of the scene.
Clearly this is different from an arbitrary light spectrum (a sum of two different light at, say, 3200 K and 6500 K will have a spectrum different from a pure 4500 K source), but can probably help. I have yet to see examples of the thing; if you have some link please edit this answer.
(Edited to take into account the comment of Dan Wolfgang --- thanks).
None of above answer explain the dual lighting vs single lighting. Single led can have twice the power of the dual led.
Regardless the brightness, dual led can control the contrast ratio of a 3d object, and the darkness of the shadow.
If taking flat copy, one illuminate from left while one from right, this makes the brightness of the flat object even.
In conclusion, dual led enable precise lighting control.