HDR photography is a technique which is used to increase the range of tones which can be reproduced in an image.
Basically a series of photographs taken at different exposures are combined using software such as Photomatix or Photoshop to produce images with more detail in the highlights and shadows.
Very dramatic effects can be created and the technique is very much in vogue among digital photographers at present, although I personally prefer to keep things looking as natural as possible. Many examples can be found on the internet which look highly unnatural - but without a doubt there is a place for this 'painterly' effect; they can make striking advertising images.
Myself, I am concerned mainly with editorial photography and my philosophy in using the technique is to be truthful to the subject and to recreate the dramatic light of a scene which would be impossible otherwise.
View my article in Outdoor Focus, the magazine of the Outdoor Writers and Photographers Guild (pages 8-11)
Read more about HDR photography at Wikipedia
Link to the Photomatix site - the software used to create these examples