A histogram, in this case, is a graph of the proportion of a tone to its value. What that means is when you look at the graph the horizontal axis shows the amount of dark parts of the image on the left of the graph and the amount of the light parts on the right of the graph. So if you have a lot of light areas the graph will bulge on the right hand side or the reverse if there are a lot of dark areas. Most photos will look like a bulge in the middle and trail off on either sides; this is called a bell curve.
It is useful to see if you are getting the full range of tones. If the histogram is right up against either side it means you are clipping off either some of the dark tones or some of the light tones. Usually this will look like a spike at one end or the histogram will be squashed up against one side.
It is also used in software like Photoshop. If you go to levels and adjust the two end triangles at the top to the edge of the histogram and follow that with moving the center one to adjust the overall brightness you will get, often, a perfectly exposed image.
I hope this explanation helps. Feel free to ask more if you want or need it.