Please permit me to rant briefly. I get incensed by the practice of most photo instructors to “dumb down” what we do. They assume people are incapable or afraid of anything technical. So they give a very short and often unintelligible description of something we, as photographers need to know, then go on. One example of this is the lowly histogram.
I’m sorry to have to tell you, but all art has a technical component to it. Photography is one of the most technical.
The histogram is like taking your temperature or looking at a graph of your portfolio performance. It is data that does not mean anything in itself but it is very useful to check. In this case, the histogram is just a measure of our image. It is valuable, but it is only one of many possible measures.
What I hope to do here is do what your dad probably did (or should have done) in this situation – tell you to get over it. You need to know this, so get on with it. 🙂
Not high tech
The histogram is not a complex, fancy piece of technology. It is just counting and marking.
Let’s say for simplicity that your image is black & white and is 8 bit depth. You know that this means the image is a grid of pixels, each having a value of 0-255. Now you decide to go through each pixel one at a time and keep track of a count of each pixel value you find. You come to a pixel that has the value 87. Go to your row of 87’s and increment it by one. You know, like 
Keep on going. If the next pixel is 127, go and increment the count for that bucket.
After you count the values of all the pixels, you will have up to 256 groups of counts. Now, draw a graph (technically a column chart) or put the data in Excel and have it graph it. If you put the numbers 0-255 on the x axis (the horizontal line) and draw a point above each number corresponding to the count you made for that number, you will have a histogram.
That’s all it is, just a count of the number of each pixel value. The actual number in each bin does not matter. What counts is the overall shape of the curve.
An example
Here is a fairly balanced black & white image and its histogram.
People would call this a “good” histogram. It shows that the tones have counts from very close to 0 to almost 255, a full range from black to white The tones are spread fairly evenly. There is a bump in the distribution of the light tones – the right side- which is natural because there are big areas of snowfields and light gray clouds.
There is no magic. You could manually follow the pattern I described and derive this yourself. It doesn’t “mean” anything of itself. It is just a way to get some information about your image.
Descriptive, not prescriptive
This is where people get confused, partly because they are misled by their instructors. The histogram does not tell you if you have a good or bad image. The histogram is descriptive, not prescriptive. That is, it is just information for you. It does not grade your image or tell you you exposed it wrong.
IN GENERAL, if your histogram shows values bunched up far at the left or far at the right, that is a warning sign. It is telling you the image may be too underexposed or over exposed. Those values at the extremes show that you may be losing data that cannot be recovered.
Whenever you see this situation it is a warning flag, not a stop sign. It may be necessary for the effect you want.
Expose To The Right example
You often hear the advice to “expose to the right“. This is good advice in general. It means bias your exposure higher – more histogram to the right – as long as there is no clipping of the highlights. This is because of some of that scary technical stuff you need to know. The dark areas of an image are more subject to noise. If you have to boost the dark areas that magnifies the noise. The best results are often obtained by overexposing a little and reducing the exposure of the whole image in post processing. Digital data retains more information when you are scaling it down than when you are scaling it up.
Expose to the right is an example of a good way to use histograms. I always have the histogram view turned on in my viewfinder. As a matter of fact, possibly the single best reason to go to mirrorless cameras is to be able to get a real-time histogram. I always check it, before and after taking a frame.
Let me emphasize again that this is information for you to use and make your own judgment. Do not let the histogram take your pictures. Keep artistic control.
Yours can look anyway you want
It is not unusual for me to shoot images that have a “bad” histogram. When I do this it is deliberate and I do not have to answer to the data police (yet).
One class of very low key images is night photography. Often these are nearly all dark with only a few points of light. This is an example:
It is hard to see at this size, but you can tell what is important from the histogram. Most data is clustered at the dark end. There is a spike at the brightest whites. These are the stars. Your instructor would tell you it is not a good histogram, but the image is exactly what I wanted. An image is properly exposed if it comes out the way you want.
At the other extreme, a high key image is almost all white. This fence in a snowy field is almost all bright values:
The distribution (the arrangement of the data values) is skewed way to the right, but not overexposed. But there is a spike at the left representing the black fence posts. Very high contrast. This is the result I wanted, so it is correct.
These 2 examples of “wrong” exposures should broaden your understanding of what is allowed. Anything that matches your intent is a properly done image.
A great tool, but just a tool.
I hope I have given you a better feel of what a histogram represents. It is just an overall look at the data values in the image. It is there for information to help you make the images you want. A histogram is neither good or bad. It is just information. Other people have given their own interpretation of histograms and their importance. This is a good one.
I am very thankful for the invention of histograms and their availability in modern cameras and post processing tools. It is an indispensable tool. I use them every day. But remember it is a tool. It is not there to tell you what you can do. You are the artist. Only you can decide the result you want.