High Dynamic Range (HDR) photos were brought to the iPhone with iOS4.1. It promised much better photos for iPhone 4 owners.
There are already applications on the App Store that do this, but now Apple has introduced their own version, and it seems to work well enough.
Below are some images with and without HDR lighting. One thing we keep in mind is that HDR isn't always necessary. The best option is to leave HDR turned on and set the device to save both your regular photo and your adjusted photo. Later, you can always just keep the one that looks better:
As you can see, the HDR tries to capture a range of shadows and highlights. It does so by using three images: one is a regular exposure, another is overexposed and the third is underexposed. The data from those three images is used to create one picture where shadows can be darker and highlights can be lights. This compensates for the more limited range that digital cameras can capture in pictures.
Remember, it's best to use HDR and have your camera save both your regular image and the HDR image. Later, you can decide which picture you like better.
For more information on 4.1, read our list of updates: Here