Heres a first attempt at some high dynamic range photography.  As I understand it so far, HDR photography allows the final image to more closely represent what the eye actually sees vs. what the camera actually sees.  Normally when you look at a scene like this where the sun is falling brightly on the peaks, and the trees in the foreground are in shadow, your eyes can still make out detail in the foreground even though it is darker.  When you try to photograph a scene like this, you have a few options on how to get the correct exposure.  You can use filters, try and tweak things during post processing, or shoot multiple exposures and combine them later like in HDR photography.  

Normally with aperture remaining constant, if you expose for the light hitting the peaks, the shutter speed will be fast, and the foreground shadows will approach black.  If you try to expose for the shadows in the foreground, the shutter speed will be slower causing the peaks to be washed out and approaching white.  If you are just taking a single shot of a high contrast scene and want to have the whole scene evenly exposed this can be a problem.     

With HDR photography you take anywhere from 3 to 9 or more exposures of the same scene and combine them all during post processing.  One shot has the peaks exposed properly, one with the dark trees exposed correctly, and other shots for exposing all things in between.  When all these images are combined later, interesting things can happen, ranging from fairly realistic representations to pretty creative interpretations of a scene.  

Anyway, so these next two pictures are a slightly tinted black and white version and a color version of the same scene.  The foreground exposure could be better, but what the hell, im still figuring out the best way to bracket these kinds of shots.  Also a scene with greater contrast would show the effect better.  Stuff like shiny chrome, and cityscapes at night are made for HDR.  Both of these images were made from 6 different exposures.