A histogram is a meaurement of brightness values on the photograph. A typical digital photograph has 256 different brightness levels per pixel. The histogram simply is a visual representation of how many pixels are dark and how many pixels are bright.

A histogram is useful becuse it shows you if the image contains enough detail in the shadows (shown in the left part of the histogram), midtones (shown in the middle), and highlights (shown on the right side of the graph) to make a good photograph.

The histogram is essentially a very sophistocated light meter. After taking a shot, you can look at the histogram and see if the shot needs to be underexposed or overexposed.

If there is a hump to the left (underexposed)

or a large hump to the right (overexposed),

even photoshop will not be able to bring out the detail of the shot that you desire.

But you ask, "why not just look at the LCD. Won't that tell me all I need to know about my exposure.?

No, is the simple answer. While the LCD will tell you about gross abnormalities in exposure, it won't tell you about anything else.

I was once shooting in dimly lit conditions, and didn't notice that my camera was set to WAY UNDEREXPOSE the shot. However, the LCD looked fine in the dim light. When I got back to the hotel, I realized that I had spent TWO HOURS in the freezing cold rain for nothing.