The dynamic range of a scene, photograph or panorama refers to the ratio between the brightest and darkest portions of the image which is accurately captured or observed. A common problem for panorama production is the large range of brightness levels found in many scenes, e.g. from the deepest shadows under a rock, to direct, unfiltered sunlight. A single exposure cannot possibly achieve detail in the shadows, and avoid saturation in the highlights.
To understand why dynamic range is such a challenge in panoramic photography, it helps to understand how the human brain eye system copes with the natural range of brightness found in the world. Typical natural scenes have a dynamic range of about 18 stops (i.e. 18 doublings), and the human eye, at a single pupil dilation, can appreciate about 17 stops (well matched to typical natural, sun-illuminated scenes, not by accident!). When you allow for the adjustment of human vision to illumination conditions, the human brain-eye system can appreciate about 30 stops of dynamic range (a factor of 1 billion:1!), from the faintest star to full-on sunlight.
By contrast, camera and display systems offer far, far less dynamic range. Good digital cameras can offer only up to 8 stops of dynamic range (i.e. 256:1), corresponding to the 8bit output in each of red, green and blue. Most deliver dynamic range well below that (see ). Using a camera's RAW mode to capture more than 8 bits of data per color can extend the range by 1-1.5 stop at most, perhaps up to 600:1. See RAW dynamic range extraction for details.
This is still a factor of ~500 less than is present in typical sun-illuminated scenes, and even that is rarely achieved in practice (see ). Film cameras offer larger dynamic range at the cost of non-linear "roll-off" of shadows and highlights. Some digital cameras apply digital transfer curves to approximate this, and certain cameras (e.g. ) have special purpose CCDs to extend dynamic range even further. The problem is even worse when considering display systems. Typical desktop displays offer about 7-8 stops of contrast (e.g. 100:1), high-end plasma TV's offer 10 stops (1200:1),
This gives you a sense of the problem, and also poignantly illustrates why it's so hard to get realistic looking moon shots or other high contrast scenes which are so easy to appreciate using your eyes, but so hard to capture using photographic techniques.
There are several methods of coping with high dynamic range, including shooting a series of exposures at different exposure times, and combining them digitally afterwards (see Contrast Blending) using 16bits per color channel (e.g. Full 16 bit workflow) to target the limited range of the output device (printer or display). There are also several interesting automatic range compression algorithms which have been proposed (e.g. Gradient Domain High Dynamic Range Compression).
Photoshop CS2 now has an internal merge to HDR function, which can assemble a bracketed exposure series into a true HDR image. There is a nice tutorial by Brian Greenstone on how to deal with this:  and a comparison of two plugins that attempt to compress a HDR image here: HDR compression