At some point in photography you are going to run into histograms. Though they may seem confusing at first, they actually provide you with a great deal of information about your photo. So what is a histogram? Histograms are used for many things but they are a graphical representation of data. In photography they are one of two representations, either a distribution of lights and darks (a tonal histogram), or the distribution of color (a color histogram).
Lets start with tonal histograms as their use will be the most evident. The left of the tonal histogram is 0, true black and the right is 255 true white. Everything in between is some shade of grey, from 1 almost black to 254 almost white. It is an average of the combination of the additive color wheel, Red Green Blue. So black is the average of 0R, 0G, and 0B and white is the average of 255R, 255G, 255B.
Now you have an understanding of where the data is coming from what does it actually tell you? Well the tonal histogram gives you a distribution of your exposure. Unless you take a picture of a monochrome setting, as in a test shot of your backdrop your histogram should reach from 0 to 255. If it reaches 70 to 255 then you are overexposed. Likewise If it only reaches 0 to say 225 then you are underexposed, and if it all sits somewhere in the middle like 50 to 200 then you are loosing contrast. The histogram will not provide you with exact numbers but you can get the idea from visualizing their respective approximates on the graphic.
Keep in mind that is just the total range and not necessarily going to be an even distribution. For example if you take a photo of a bride on a white background very little of the distribution will be down at 0, just the really dark shadows and if her hair is black it will register in the left of the histogram, but the vast majority will be in the right. This is an example of "high key" photography, likewise if you are working in "low key" photography then the histogram will be very heavily weighted to the left but should have some elements on the right, reaching all the way to the 255 edge for the specular highlights or white elements of clothing.
One last trick you can use for judging exposure is to use the histogram as your light meter. The way to do this is to put a diffuser in front of the camera lens and shoot an image from where the subject would be facing back to where the camera will be when shooting. You can use the diffuser for a soft box for this by turning off autofocus and wrapping the fabric over the lens and holding it in place. This mixes all of the light coming into the camera evenly and will give you a single spike in the histogram. This spike should be In the center, or just slightly left as your diffuser may absorb a half a stop or so of the light coming in. This lets you know your camera settings are set correctly for the light falling on the subject. You can then take a second test shot of just the background and look at the histogram for that. In most photography you will want the background to be shifted to the left as our eyes will focus on the lighter sections of the photo. If the background is to the left of the histogram then the subject will be the lighter section of the photo. High key photography is an exception, here the background should be shifted heavily to the right.
The color histogram does the same thing but for each of the three colors, along with showing the areas of overlap and the kind of mixing they have. On many cameras you can actually look at the three colors individually as well. This will give you an idea of the distribution of red, green and blue. If you are taking a landscape photo of a grassy plane with a blue sky then your histogram should be very low in the reds while being quite high in the distribution of greens and blues. As you begin to understand this relationship you will be able to judge color balance and tint in the images you are looking at.
Something to remember, the histogram is a tool not a judge. Understanding it and using it properly should expand your creativity, not limit it. Think of it like "The Pirates Code" from Pirates of the Caribbean it provides a guideline and not hard and fast rules. The machinery does not have artistic vision, you do. Understanding what the histograms are telling you will help you reach your vision, it should not dictate what that vision is.