HDR stands for High Dynamic Range.
When a photographer is faced with a scene that has close interesting objects in the foreground and distant interesting objects in the background, each of which has different lighting conditions, and she wants to capture both foreground and background in focus with the correct exposure, the difficult decision is: what f stop should I use. The choice has tremendous effect on depth of field, hence the focused zone, and on the correct exposure for each part of the scene.
Usually any complex scene has a “best” combination which changes as one tracks from foreground to background. That means that there is no way to make a single choice which will work for the whole scene.
Enter High Dynamic Range photography or HDR. This is a technique which imagines the scene divided into different areas, organized by distance from the camera, and based upon what combination of f-stop and exposure is best for that sector. A series of photos with the “sweet combination,” tracking through the photos from foreground to background, is then taken.
Using specialized software, the photo series is combined into a single image; only the “sweet zone” from each photo is included. When the series of photos is stacked, the f-stop/exposure combination is correct from foreground to background so that the scene is sharp and clearly lighted from foreground to background.
You can learn more about HDR from Trey Ratcliff.