The above shot was taken in 2008 in Las Cruces, NM. It was an overcast, windy day, with great big gray clouds rolling in over the mountains threatening their wrath. I took bracketed shots all over the place, hoping to do this "HDR" thing I had heard about. I made some weak attempts at in-photoshop HDR at the time, and remember being disappointed.
I have learned a thing or two about HDR since then. HDR stands for "High Dynamic Range." It basically refers to an image with way more color and light information than your computer monitor can display.
HDR is an attempt to fix a problem that plagues all photography. The photographic sensor is never as good as the human eye/brain. A person can look at the scene above and see the mountains, the sky and the foreground flowers with the same clarity. A camera is not that good and usually you would have to choose what you wanted correctly exposed: the mountain, the clouds or the flowers.
With HDR, you can (theoretically) have your cake and eat it too. A lot of times this is done by bracketing in camera and actually taking 3 images at different exposures. Then these images are combined into an HDR image which has way more color information than your monitor can display, and you use software (I used Photomatix) to create an image that (hopefully) has everything correctly exposed.
I won't get into technical details, since I'm far from an expert (and maybe I will post a how-to in the future). I created this HDR with one shot (instead of the usual 3 or 5). Since it was RAW, I was able to create my -2, 0 and +2 exposures (exported as JPEGs) off the one image. In Photomatix I played with it until it looked close enough and then exported the Photomatix tone mapped image and the 3 exposures to Photoshop as layers. The sky was a bit neon so I used a layer mask to mask through the HDR layer to tone it down. My original shot had blown highlights in the clouds, so no matter what I did could bring some of the cloud texture back.
The key with HDR is realizing that it is not a magic bullet for photography. It is just a way to capture multiple exposure settings in one image. Great for landscapes on a cloudy day, indoor shots with bright windows, or anywhere else where you want to retain details in the shadows and highlights.