HDR stands for High Dynamic Range and although it is a concept more than ten years old it is new for me.
Several processes are trying to mimic the way we see things: moving pictures, photographic prints, computer displays, etc. The underlying idea is that an accurate representation is achieved when "it looks like the real thing".
Unfortunately, neither prints nor displays can exhibit the dynamic range required for a picture to look the same as the original. While our eyes have a dynamic range of 10000 light levels, a print can only represent around 100 different light levels. On the other hand, the whole range our eyes can see is around a million different levels, just not all at a time (i.e. you need your vision to adapt when you go from a dark place to a sunny one).
While photographic cameras (either chemical or digital ones) can do a great job capturing a scene in one shot, some compromises are done down the line. The end result is that some saturation and some range compression happens in every shot.
If you want to keep good detail of a dark area you select the proper exposure values but then the areas with the more light will appear burned. If you do the opposite then the darker area detail is lost but the burning has been avoided.
If one exposure value is not enough, then use more!! This is the idea behind HDR. You can achieve a higher dynamic range by taking several shots of a single scene using a varying exposure (usually changing the shutter speed). Later, you can combine these several shots into a single image with much higher dynamic range.
Sounds good, but there is one caveat: you cannot either print this photo or show it on a display. Why? Because these procesess lack of the required dynamic range.
What it can be done is to create a new low dynamic range photo from the HDR one that highlights the improvements obtained by all this. This is done by a process called tone mapping which uses different math functions to map the values of HDR pixels into a system with much lower dynamic. There is quite room for creativity here, so don't be surprised that some photos obtained by process look actually quite synthetic.
There are several programs that can help you with this process. I have tested Photomatix and ArtizenHDR. Photoshop 9 CS2 also includes support for HDR photography. And no, The GIMP cannot help you with this process as it is designed for low dynamic range photos only (8 bits per color per pixel).
Have a look at HDR photos on Flickr.
If your camera allows RAW format, then you can obtain images with higher dynamic range already (usually 12 bits per color per pixel) from just one shot. No wonder everybody is so excited about this feature on digital cameras (too bad I've just bought a DMC-FZ7).