You will find lots of discussion about this technique on the web
But the main thing is that you can increase the detail in the shadows and highlights using the technique.
The human eye sees some 12 different F-stops of light. The camera, on a good day, and a good camera, can record about seven F stops. That means something has got to give, either detail in the shadows, or in the highlights. HDR attempts to correct for this reality.
You need a camera that can record different exposures, or ISOs, of the same image. The Fujifilm X-Pro 1 allows you to record a single image with three different settings, without the use of a tripod. Then in post processing software will merge the photos, producing an image with a wider range of tones. Here are two images, one b and w, the other color, of the same image taken at Pioneer Town and processed using Nik’s HDR program. I am sure there are many other programs that will perform the same actions. I know that Photoshop provides a combination-of-images program.
This is NOT a great capture, meaning it’s an uninteresting subject matter, and not very well composed, but it does show you the gradation of tones, from very white, to very black, in the black and white version, with a lot of information between, and in tonal range of colors in the color version. Had I used only one of the images, there would have been a loss of detail in the shadows, or in the highlights, or both. HDR gave me a greater range of tones and colors. Click on either photo and it will loom larger.
Below my comparison are some others provided by other photographers, and shown by permission.
Hope this explains this photographic tool.