HDR, or High Dynamic Range, photography is different things for different photographers.  For me, it's a way to radically increase the dynamic range, depth and detail of my photographs to get an image that's much closer to what the human eye can see than is usually possible with a single exposure image.  If one is shooting in a studio, or in some other controlled-light situation, the shortcomings of the DSLR sensor can be dealt with by placing light sources as needed.  But I work outdoors, and don't have the ability to control Mother Nature's lighting choices, so for me HDR is amazing.

I always shoot in Camera Raw, and I shoot from 3 to 9 exposures of every image I want to capture.  Camera Raw captures lots of information that a jpeg image doesn't, so if one is serious about image control, there's only one way to shoot... Camera Raw.  However, Camera Raw images don't look very good.  Here's an example.  This is the middle exposure of a 9-image set I shot at dawn at Atlanta Country Club in October.

Less than exciting, certainly, but with 4 exposures on both sides of this middle exposure, I have plenty to work with.  Already, you can see that the sky is white and the shadows fade to black pretty quickly.  Not the goal, certainly.  So, the first step is to use tonemapping to expand the dynamic range, allowing me to hold details in the highlights while opening up the shadows so we can see what I actually saw on site.  Here's a tonemapped image.

As you can see, tonemapping makes a huge difference, opening up the shadows and bringing a bit of color back into the sky, but we're still not where we want to be.  At this point, I typically open the image in Photoshop and begin to add contrast, detail, and a few other things... like a sky that seemed appropriate... to yield an image that is much more like what I saw and felt on the morning I took this shot.  Here's the final image in the evolution of this HDR image.