HDR Before and After by www.lightphotographicworkshops.com

In image processing, computer graphics, and photography, high dynamic range imaging (HDRI or just HDR) is a set of techniques that allows a greater dynamic range of luminances between light and dark areas of a scene than normal digital imaging techniques. The intention of HDRI is to accurately represent the wide range of intensity levels found in real scenes ranging from direct sunlight to shadows.
If you have ever photographed a high contrast scene, you know that even the best exposure will typically have blown out highlights and flat shadows. Shooting HDR and using Photomatix (software) offers two ways to solve this problem: 1. HDR Tone Mapping: Reveal highlight and shadow details in an HDR image created from multiple exposures. 2. Exposure Fusion: Merge differently exposed photographs into one image with increased dynamic range.

Benefits for photographers include 1. saving on lighting equipment with no need to acquire expensive  equipment and carry it when you shoot high contrast scenes. Just enable the Auto Exposure Bracketing feature of your camera, and merge your photos into an image with extended dynamic range.
2. Great pictures on cloudy days Shadowless hazy sunlight or an overcast sky usually results in dull-looking photographs. The tone mapping tool of Photomatix Pro can turn them into great-looking images. Check this image as example.
3. Well exposed panoramas.
A panoramic scene is almost always a high contrast scene you can’t limit your view to areas with the same brightness when shooting a 360° panorama. By taking views under several exposures and processing them, you can create a panorama that will show details in both the dark and bright areas of the scene.