If you are unfamiliar with high dynamic range photography the image above is one example. In essence, high dynamic range utilizes a series of images captured of the same scene but with different exposures. It allows software to assemble, or tone map, a resulting image that contains an exposure range greater than the camera can handle with a single exposure. Let's take a look at what I mean.
The scene above contains a sculpture of three anchors. As you can see the anchors are situated under the shade of a tree. In the background are some buildings in open sunshine. The scene above is closer to how we would see a scene with our own eyes. That's the beauty of the human eye. We can discern so much more information, from bright light to deep shadow. Unfortunately a camera does not have that ability.
If the technique for assembly requires additional exposures you simply create some in between, five instead of three, seven instead of five. However, I would argue that you really are not gaining all that much by generating more exposures, but that's an argument that goes beyond the scope of this article. However, you can clearly see that one single exposure can not capture the full range, light to dark, that exists naturally in that scene. So this is a clear cut example of when HDR is of benefit. This is what HDR was designed to do.
As with any other tool, HDR has gone beyond the practical and and the technique of tone mapping has been used successfully with single exposure images as well as with scenes that do not have an exposure range that exceeds the capabilities of the camera. In these cases the use of HDR falls into the realm of artistic interpretation and is used to visually enhance an image, not unlike using Photoshop or other photo editing tool.
While this is a rather simplistic explanation hopefully it gives you a good introduction to a technique that is worth exploring. I wrote an article about two years ago regarding bracketing sequences. It's a bit outdated now since both software and hardware have gotten better, but it might still be worth reading.