HDR (High Dynamic Range) photos increase the range of brightness in your photos by taking two or more pictures at different exposures, then combining them.
The human eye is more sensitive to light than a camera. It can detect details in both deeper shadows and brighter areas. To compensate for this you can take two or more photo; some under exposed to make the light areas detailed, and some over exposed so that the dark areas have more detail. Then you use software to combine the best of each.
The technique can result in anything from striking (but fake looking) to subtle enhancement of the image. Apple being Apple, they go for the second.
So if it makes better photos, why bother with an on/off switch?
Because if there is any motion in the subjects it can cause blur or even double imaging (in extreme cases). It gets worse as the amount of available light decreases, and the camera has to take longer capturing each image.
So, if your subject is still, like a landscape, turn on HDR and enjoy better quality images. If it is an action shot, or fidgety kids, then turn it off.
Or you can leave it on all the time, but turn on 'Keep Normal Photo' in Settings > Photos & Camera. This will keep the best single exposure and the HDR version, so you can choose after the fact which looks best. Of course, this gobbles up your storage faster, and can make the Camera Roll a bit cluttered.
