HDR (wiki) is short for High Dynamic Range. It is a post-processing of taking either one image or a series of images, combining them, and adjusting the contrast ratios to do things that are virtually impossible with a single aperture and shutter speed.
Photography purists might see many HDR images as gaudy & cartoonish but I really dig the way they bring out a new experience of the subject. The hyper-realism of some HDR compositions seems to almost virtualize the world blurring the lines even further between real & synthetic.
To take your own HDR photos, check tutorial here