Lets start with what exactly 'Dynamic Range' is.
When you look at a scene, there will probably be a range of how bright things are. We can assign a brightness value to each thing/area...in EVs (exposure value). So for example, the sky might be EV12, the landscape might have areas of EV8, EV6 and EV4. So to calculate the dynamic range of the scene, you take the brightest value and subtract the lowest (12-4) and we come up with a dynamic range of 8EV (or 8 'stops').
Now we need to realize that our cameras are only capable of recording detail within it's own dynamic range. For the most part, digital SLR camera are capturing about 4-5 stops (while maintaining good quality).
So when you go to take a photo of a scene that exceeds your camera's dynamic range...you will have to make a compromise. If you expose for the shadows, the highlights will be blown out (white). If you expose for the highlights, then the shadows will be black with no detail. So it has been our task, as photographers, to make this choice and expose for what we deem to be the most important parts of our scene (or do something to alleviate the problem).
One way to get around this problem, is the HDR technique. (High Dynamic Range). With this technique, rather than choosing one exposure, you take several photos at different exposure values...exposing for the shadows and the highlights. You then use software to take the best parts from each image and combine them into one image, which will have a greater dynamic range than you could ever capture in a single photo.