The computer measures brightness in an image on a scale from 0 (black) to 255 (white), everything in between is a shade of gray. The histogram is a graph of an image's brightness values from 0 to 255 on the x axis vs. the number of pixels along the side (y axis). You can see in this histogram that most of the pixels are in the gray areas in the middle. There are no black pixels in the image and a sudden spike of white pixels at the 255 mark.
The histogram is very useful to see what the dynamic range of your image is. It helps you identify a black point and a white point while correcting the contrast and color in an image. The basic goal is to get the image to have a ranges of pixels filling the entire histogram from 0-255. You can tell when an picture was scanned on a cheap scanner because the pixels will be squashed towards one end or the other (usually the dark end).
