The horizontal axis represents the range of brightness from 0 (shadows) on the left to 255 (highlights) on the right. Think of it as a line with 256 spaces on which to stack pixels of the same brightness. Since these are the only values that can be captured by the camera, the horizontal line also represents the camera's maximum potential dynamic range.
The vertical axis represents the number of pixels that have each of the 256 brightness values. The higher the line coming up from the horizontal axis, the more pixels there are at that level of brightness.
To read the histogram, you look at the distribution of pixels. An image that uses the entire dynamic range of the camera will have a reasonable number of pixels at every level of brightness. An image that has low contrast will have the pixels clumped together and have a narrower dynamic range.
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