An image histogram is the distribution of image pixels. It is made by counting how many pixels have value 0, how many have value 1, and so on up to the maximum allowed pixel value. For these landsat images the maximum value is 256.
Here is the histogram for the above image:
The shape of its histogram can give important information about an image. In this example the histogram has two peaks, a low narrow peak, and a broad higher peak. Low pixel values, that is values on the left side of the graph, represent dark pixels. Higher pixel values (toward the right) mean brighter pixels.
Also each pixel covers the same area in the image. So this example histogram is telling us that there are a number of pixels that are much darker than average in this image. The darker pixels are not as numerous as the brighter ones. The histogram tells nothing about the distribution of these darker pixels, they could be scattered over the image or grouped together and the histogram would look the same.
Looking at the image makes it clear that the left peak of the histogram is made up of the pixels in the area covered by water. The almost complete separation of the peaks shows that this is a good band to distinguish between land and water. The image shows that all or almost all the pixels in the left histogram peak are part of Liberty Reservoir. The vertical line in the histogram, at about pixel value 16, is a good place to divide the two peaks.
The number of pixels of values 0 through 15 is 8598. Each pixel was previously determined to be 28.5 by 28.5 meters, so the area of a pixel is about 812 square meters. The total area of Liberty Reservoir as measured in band 5 of this image (using pixel values up to 15) is 8598*28.5^2 = 6.9837e6 sq meters. One sq Km = 1e6 sq m, so the area is 6.98 sq Km or about 2.7 sq miles.
The same area may be found by thresholding the image at 15 and lower and counting the selected pixels.