HDR stands for High Dynamic Range.
The way our eyes/brain work together to render and images is completely different to how a camera does it. As a result, on a very sunny day it's very difficult for the camera to correctly expose dark foreground and a bright sky with the use of say a ND filter.
To create an HDR image, you would need to take at least 2 shots of the same scene, one over exposed, 3 shots are better but more can be used.
You would then need to use photoshop, photomatix etc to combine the images. The software will then merge the images using the tones/exposure from each. This *should* then get all areas of the image exposed correctly, in a way that's very difficult/impossible to do in camera.
However, there is a tendency if *over done* to make the image to appear surreal or cartoon like.
To get the images you generally need a tripod and remote to ensure the camera doesn't move between shots. Most cameras have a "bracketing" mode which will take 3 images in close succession where you can set the exposure range, for instance -1, 0, +1