Definition: A histogram is a graph that depicts the tonal range of an image. The far left column represents 100% black pixels and the far right represents 100% white pixels, with all other tones spread in between. Most scanning software, photo editing software, and some digital cameras allow you to view an image's histogram. (Continued below...)
A histogram that shows more weight at the left of the graph represents a dark image, also called a low-key image. A histogram with more weight to the right of the graph represents a bright, or high-key, image. An image with a low-key histogram may be overexposed, and an image with a high-key histogram may be underexposed, though this is not necessarily always the case. Your eye--not a histogram--should always be your final judge. A histogram that shows a large flat area on either end of the graph, however, is most likely in need of some adjustment as you can see from the example below.
The flag in this image is supposed to be white. It is clearly underexposed.
The histogram makes it very obvious when you see the large flat are in the highlights
portion of the graph. The histogram can also serve as a guide to let you know
how much correction to apply.

Most photo editing software has an Auto Color or Auto Levels command that can
quickly fix these types of problems. Here Photoshop's Auto Color command was
used and you can see the change to the histogram. With the majority of the graph
weighted to the right, this is a fairly high-key image.

This histogram of this image shows it is a low-key image, though the color and
tone does not need correcting.

Images that have been heavily edited often have spikes or gaps in the histogram
such as the one shown here, taken from a artistically styled photo.
The histogram is just one tool which can be used in evaluating what kind of corrections may need to be done to an image. Use it as a guide, but don't let it become your sole focus.
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Also Known As: levels graph, tonal chart
Related Resources:
Elsewhere on the Web:
Understanding Histograms
"Possibly the most useful tool available in digital photography is the histogram. It could also well be the least understood. In this article we will look at what a camera histogram tells the photographer and how best to utilize that information." By Michael Reichmann for The Luminous Landscape.Adjusting the Histogram
An excellent page for demystifying the histogram.

