Dynamic range refers to a range of values between dark and light greater than that which is possible in normal digital imaging. The technique is the capture of a series of photos with different exposure values, and then uniting the images using a software tool.
The origins date back to film in the 30s and 40s when Charles Wyckoff made the technique famous on the cover of Life magazine with a series of nuclear explosion photographs.
But it was not until the 1990s when graphic designer Paul Debevec (famous for his work on the Matrix) came up with the process of tone mapping a set of bracketed exposures that the technique really took off. The first attempts were very exagerrated, a technique which is still popular today. These are the examples seen here which are almost cartoonish, verging on surreal.
There are various software tools to use to get the effect, Photoshop and Photomatix are probably the best known. I myself much prefer Photomatix.
Essentially HDR involves you doing a series of bracketed exposures. Obviously you need a tripod because any movement at all will be exaggerated when you merge 3 or more images together. The number of images you can merge is very much dependent on the number of values your camera will allow in a bracketed sequence.
For a more realistic image, 3 is the best.
What you will do is to bracket your camera to the maximum values possible. This will give under exposed, normal, and over exposed images. You do very minimal adustment to the RAW files. The software will then merge the images and you can tone map or detail the images in that application.
The best use of HDR for landscapes is when you can capture some detail in the overexposured image at around 2 seconds. This will produce an amazing result especially if water is involved in the shot.
HDR allows you to capture the detail in both the high and low value light and combine that into the normal exposure to make a compelling and eye drawing image.
Have fun experimenting with HDR.