Langfords
pg 258
It is essential to be able to understand and read what the histogram is telling us.
The histogram is a graphical representation showing the distribution of tones in your photograph. The very left point represents absolute black, the right point represents absolute white.
A good histogram typically looks like a mountain range, perfectly spanning the width of the graph but dropping down at the peripheries. An overexposed or underexposed image will be one sided and at its worst look like a cliff edge (representing extreme areas of clipped highlights or shadows).
Adobe
helpx.adobe.com/photoshop/using/viewing-histograms-pixel-values.html
A histogram illustrates how pixels in an image are distributed by graphing the number of pixels at each color intensity level. The histogram shows detail in the shadows (shown in the left part of the histogram), midtones (shown in the middle), and highlights (shown in the right part) A histogram can help you determine whether an image has enough detail to make a good correction.
The histogram also gives a quick picture of the tonal range of the image, or the image key type. A low‑key image has detail concentrated in the shadows. A high‑key image has detail concentrated in the highlights. And, an average-key image has detail concentrated in the midtones. An image with full tonal range has some pixels in all areas. Identifying the tonal range helps determine appropriate tonal corrections.
Photography: the new basics
pg 149
Exposures should be judged by calling up the camera's histogram. This is a bar chart that displays the number of pixels in the image that have any one of 255 tones between black and white. Reading this can give you a precise guide to the exposure.
The left side of the histogram represents the darker tones in an image, with black the far left, lighter tones to the right, and pure white at the far right-hand edge.
If the majority of bars are shifted to the left - slightly underexposed
If the majority of bars are shifted to the right - slightly overexposed
High key - pale and delicate
Low key - dark and sombre
If the bars stack up against the end of the histogram, you have lost detail in this area, indicating blown (pure white) highlights or blocked-up (pure black) shadows that contain no detail.
Dynamic range
The range of tones between black, the darkest shadow, and white, the lightest highlight in a subject. In photography, it is most commonly given as the number of f-stops between those two tonal extremes.
pg 190
If a histogram displays a one map that is sitting between shadow [0] and highlight [ 255] points, it will have a soft flat appearance.
pg 191
An underexposed image will show detail missing from the shadow end of the histogram resulting in many more tones reproducing as black.
An overexposed image will show detail missing from the highlight end of the histogram resulting in many more tones reproducing as white. When printed, this means no ink will be placed on the paper, giving ugly clear patches in these parts of the image.
If you control the exposure so that the histogram is kept slightly towards the highlight end but without clipping the brightest parts of the image, it will help minimise noise in the image.