Histogram is a useful tool for helping you analyze, at a glance, how the information and exposure data in a photograph is distributed. It shows the luminosity range of the image along with how it is distributed. The horizontal scale of the histogram measures exposure latitude, and the vertical scale measures quantity: it tells us how many pixels in the image have a specific luminosity value. While the horizontal scale is measured in absolute values  (0 to 255) the vertical scale is effected by several factors: the color space, bit depth, and if you are shooting jpegs, the compression level. So the further to the right you expose without clipping the highlights, the greater amount of differences you are recording. Once you have recorded the image you can start teasing it apart to see the differences in tone.

When you start with an underexposed image and have to lighten it during processing you create gaps between the steps because you have fewer and cruder gradations of information recorded. Visually this shows up as banding (abrupt changes in tone). Noise begins to visibly become more apparent, too. Yes you can reduce noise with software, but at the expense of detail and time. So exposing correctly in the first place results in both better image quality and saved time.

Many cameras today now offer the option of either viewing a simple composite luminance histogram or if you choose, to let you examine a per-channel view to see more precisely what the exposure level is in each color channel. If you fall into the class of people who believe that the more information you have to work with, the better informed your decisions are, you should explore this option.

More advices on using histogram, differences in histogram in various color spaces such as Pro Photo, Adobe RGB, sRGB in How To Read and Understand a Histogram (Professional Photographer Magazine Web Exclusives)

In addition, a couple of  tutorials on using histogram.