Contrast enhancement is applied to images where there is a lack of contrast. Lack of contrast manifests itself as a dull or lacklustre appearance, and can often be identified in image histograms. Improving contrast, and making an image more visually (or aesthetically) appealing is incredibly challenging. This is in part because the result of contrast enhancement truly is a very subjective thing. This is even more relevant with colour images, as modifications to a colour, can impact different people differently. What ideal colour green should trees be?
Here is a brief example grayscale image and its histogram.
It is clear from the histogram that the intensity values do not span the entire range of values, effectively reducing the contrast in the image. Some parts of the image that could be brighter, are dull, and other parts of the image that could be darker, are lightened. Stretching both ends of the histogram out, effectively improves the contrast in the image.