Let's start with what "histogram" means in the non-photo world.
A histogram is a graphical/visual representation of a set of data. For example, if you made a survey of riders on Fromme and what size bikes they ride, you could come up with a set of data like this, then turn it into a histogram it would look like:
Now let's do a "survey" of a photo.
Instead of "bike size" you would have something like "light range", while "frequency" (how much of something you have) would stay the same (in any histogram, frequency is always there but what you are plotting frequency against will change). Under "light range" you would have Blacks, Shadows, Exposure, Highlights and Whites. Now if we plot it out, you would have on the x-axis (bottom): Exposure in the middle, as they are your mid-tones, then Highlights to the right, your "upper" mid-tones, then to the right of that, your Whites. To the left of the Exposure/mid-tones, you have shadows, your "lower" mid-tones. And finally to the left of that you have your Blacks.
Now once you plot it out against the frequency, ie how much blacks do you have, how much shadows, whites, etc, you end up with a histogram.
Here's a simplified "photo" histogram. A photo that would create this histogram would be on the dark side of things, with some "neutral" areas. You can see there are a lot of Blacks and shadows, whereas there are almost zero highlights and whites
This histogram tells me I have a lot going on in the Blacks (left-most) and the Whites (right-most), but not so much of the mid-tones area (Shadows, Exposure and Highlights). If you look at the actual photo, you can see it has a lot of bright whites in the background, some very dark spots, the Blacks, in the clips, and very few mid-tones. The histogram takes this information and creates a graph out of it.
Now take a look at this photo. You can see that there are no bright (whites) spots, and the back of the grill is very dark, in this case it is clipping. The detail in the food is not lost through clipping, and there are some "lower mid-tones". If you look at the histogram, it shows you that there are a lot of Blacks (back of the grill, lower right corner), some shadows (on the food, bottom of the grill), a small bump in the mid-tones (the food), and the Highlights and Whites are basically non-existant in this photo.
Now let's take a look at the tone curve for the grill photo
The line represents where things are at right now. When you push a section of the curve up, it makes that section brighter, when you push it down, darker.
Now for this photo, I've made everything brighter, since the whole photo was leaning towards the Blacks. You can see that the food has started clipping, the lower right corner wasn't too dark so there is a little recovery in it (it was classified as "Shadows")…but the back is still clipping. Nothing I can do about that, it was way too dark when I first took the photo anyways. (By the way, I wouldn't publish a photo that looks like the way I edited it. It is in no way complete).