Here's the good news for most of you: many digital cameras don't let you see a histogram. You're done now — you may get on with your life.
For everyone else, here is a simplified approach to understanding the histogram.
What is a Histogram?
I like to thing of a histogram as a visual representation of the light and dark elements in your photograph. Since I am a visual person, it helps me when I can see a diagram, rather than being forced to interpret a lot of nonsensical numbers.
The continuum from left to right represents the tones in the image from dark to light.
Let's say you take a photo during the day — there are a lot of middle tones, but no areas that are especially dark or overly bright. The histogram will look like a bell curve, high in the middle and tapering at the ends.
Now you take a photo at night — the majority of the image is black. You will see a huge peak toward the left of the histogram, which tapers off to nothing on the left-hand side.
Finally, you take a shot of a building wall that is predominantly white. Got this figured out? The peak of the histogram will be over to the right side, tapering off to nothing on the left.
Histograms and Exposure
We have a sense of how a histogram represents the amount of light and dark areas in a photograph, but we want to apply this to exposure.
Let's go back to that scene where there are a lot of midtones, but not a significant amount of shadow or light areas. This histogram should look like a bell curve, and the peak of the histogram should be in the middle of the graph (as in the example above).
Now let's say you under-expose your photo. This is similar to taking a photo at night. The histogram will still look like a curve, but the curve will be shifted over to the left. The peak of the curve will also be higher. Even though the scene was not dark to begin with, you have made it dark by under-exposing the photograph.
Conversely, an image that is over-exposed will show a histogram that is shifted over to the right. The entire image is too bright. This particular image is especially over-exposed, since the histogram just keeps going up on the right side — there is no peak.
Checking Histograms as You Shoot
You can get the most out of a camera that displays histograms by changing the photo review mode so that this histogram always displays. The photo review mode is what lets you see the photograph you have just taken on the camera's LCD screen.
Right after you take a photograph with your camera, the photo you just took appears on the LCD. Most cameras let you adjust the duration that the image appears. A few cameras will let you display a histogram every time you review an image. So how does this help?
When you check the histogram, you can instantly tell if you have over or under-exposed the photo you just took. If the peak of the histogram is to the left, it is under-exposed and you need to adjust your camera settings to let in more light. If the peak of the histogram is to the right, the image is over-exposed and you need to change settings to let in less light.
If the peak is right in the middle, or evenly distributed then congratulations! Your photo is properly exposed.