HDR is a method of processing that combines several exposures of the same shot. By doing so, the ranges between dark and light are better represented. Unlike our eye, the camera cannot effectively process the wide ranges in intensity that exist between light and dark. HDR allows you to do this.
The photo can further be manipulated to allow other effects such as enhancing colors. This "grunge" type of appearance can give it this surreal, dreamy look. Not everyone is a fan of this kind of HDR but it does give a unique look to the shot.