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The Histogram Functions modify an image or a selection within that image based upon its luminance histogram.
The Histogram Window doesn't do anything in and of itself, it's a tool designed to help you decide what you need to do to improve your image.
The histogram window displays a graph of the color values of the active window. The display is usually in RGB and the luminance. Zero luminance is black while full luminance is white. The numbers at the top of the window display the number of pixels that match the histograms max., min., and average values. The spectrum for a color is on the horizontal axis while the portion of the image's color that matches that spectrum is displayed on the vertical axis.
The check boxes at the bottom allow you to turn off the graphing of certain colors or the luminance. Click on the red check box in the histogram window to the left to see how the graph displays with the box unchecked.
To apply one of the functions to the active image:
Some examples of the Equalize Function

Original picture, taken with an old Pentax SLR, the negative transferred to cdrom PCD format, and converted to jpg. (ok... so it was a new Pentax, but it's old now since the picture was taken in 1967) :)

For this example I selected an area of the sky using the magic wand, tolerance set to 20, feather set to 9. I had to hold in the shift key to include the area inside of the bridge girders in the selection.

Applying the Equalize Function to the selected area gives a nice highlighted affect, and accents the bridge. I applied a soften affect to the highlighted area using the retouch/soften tool, taking care to not retouch the bridge. This removed the splotchiness around the highlighted areas edges.

With this example, I took a slightly different approach. Using the magic wand tolerance set to 20, feather set to 0, I selected the black 'tree' area of the image. I then inverted the selection and applied the Equalize function, resulting in everything but the trees being equalized.