HDR stands for High Dynamic Range. It is the process of taking 3 or more captures of the same scene at different exposure levels. You then use a program like PhotoShop or Photomatix to merge these images together. It is meant to more closely resemble what the eye sees. For example, if you look at the first post in this thread, you will see that the first pic of the GT has a washed out, or overexposed, sky. The second pic, which is actually made up of at least 3 different exposures, captures the detail in the sky, the foreground, the whole image.
Some people have confused true HDR photography with fake tone-mapped images. You can't truly make an HDR unless you have multiple exposures taken by the camera. Many people run 1 image through PS and great multiple exposures that way, but that is not really HDR because the camera never captured any information to display in the original image, so there is no way to bring back that lost data.
Hope this makes sense. It can become a little convoluted at times.