HDR has been around for pretty long since it can painstakingly be done manually in photoshop all this while. Its like blending a few exposures to create a clearer, brighter.. hard to explain. Google it.
HDR is a digital image processing technique to represent/create the illusion of more "dynamic range" than your sensor can capture; and dynamic range is the spread between the brightest and darkest in a picture.
Examples of large dynamic range scene are like shooting into the sun at sunrise or sunset or in any high contrast situations. Without HDR, you either get deep shadows with no details, or blown highlights with also no details. With HDR you get details in both while possibly retaining the sensation of a natural visual experience. Alternatively the very same techniques can be used to get very surreal pictures.
There are many techniques of doing HDR, the most common and easy to use is Photomatix from HDRsoft.
And note that all imagery are artificial, including those "direct from cam, without retouching", etc, etc. So dont get too anal about trying to make HDR "natural". Just be artistic about it, as with anything else in life.
Addendum: Just to add, HDR has been around for as long as there was photography. In analogue times, people use GND filters to overcome the mismatch between a scene's and the capture medium's dynamic range. Use of flash fill in is also another example of trying to narrow a scene's large dynamic range.