HDR is an awesome technique which produces photos which capture a much wider dynamic range than standard photos, and which can in many cases look more like very expertly done paintings than photos. It does this by combining multiple photos which are taken sequentially with different exposure settings. (This is known as autobracketing.) So one photo might be exposed for the highlights and another for the shadows, and the HDR software would then combine the best of the two photos (or more than two) to create an image which looks better than either of them alone.
The main problem is that HDR really only works well when there aren't subjects which are moving substantially in-between the different shots. Some HDR software can help to "erase" such subjects to some extent, but HDR is still more of a technique for still life and landscape images than for action photos.
Fortunately, I've found a software program which seems to do a superb job of mimicking the look of HDR photos, without the need for multiple exposures. It's called Topaz Adjust. Needless to say, it's a real boon for action photographers, but also useful for older photos for which there are no bracketed exposures. Or for modern photographers who possess cameras which lack autobracketing capabilities. Here are some very impressive links regarding the program:
Topaz also makes some other cool programs, such as Simplify. Furthermore, their website has an aweseome online gallery showing just what the software can do in the hands of photographers and artists who know what they're doing. Check it out!