HDR is the acronym for High Dynamic Range, which basically means that you take 3 (or more) pictures of the same spot but with different exposure, so that you cover light definitions, midtone definitions and dark definitions. Then you put those pictures together with the help of either photoshop or photomatix (my choice) to get a picture which covers all ranges. The picture will have well lit lightning and look a like a painting.
Ofcourse there's a lot more to the picture than this. You still need to tonemap and enhance certain features to make it look like my example, but that's HDR in a nutshell.