High dynamic range imaging, also known as HDR, is a technique that takes multiple exposures of an image; overexposed, underexposed, and in the middle, then combines them together in order to bring out all of the details of that photograph.
When should you utilize HDR? The best uses would be with landscapes & outdoor portraits. For landscapes, HDR will combine an underexposed sky with an overexposed foreground to highlight the best parts of that image so that the sky wouldn’t look blown out and the foreground wouldn’t be too dark. With portraits shot outdoors in harsh light HDR will remove the shadows on the face of the subject and bring out details in the overexposed background. You should avoid HDR if you are trying to capture motion, when dramatic contrast is desired, or when you need to utilize a flash. If you are working with vivid colors you should avoid shooting in HDR, as it can desaturate your image, and instead experiment with applications that apply HDR-like filters, mentioned below.
With the iOS 4.1 update last year, Apple introduced HDR to their Camera app that, when using the back camera, takes three images quickly all in a row and combines them. Often HDR images can appear fake and a bit harsh, but the built in HDR option by Apple tends to tone down the effect, providing a great way to get evenly exposed images. An application alternative to the built-in Camera HDR is True HDR ($1.99), which combines two images and also has basic image editing built in.
Of course, if you love the extreme HDR effect and want to experiment further with it there are applications that utilize filters in order to attempt to reproduce the HDR look such as Pro HDR ($1.99), or iCamera HDR ($0.99 - sale price), & Camera Plus ($0.99 - sale price).