Simply put, a histogram represents your image’s color and contrast ranges on a graph.
At a glance, you can see if your image is properly exposed or not. Here are 3 examples of images with their histograms.
From these examples, it’s clear to see that when most of the histogram information is to the right, the image is over exposed and when the information pushes more to the left, the image tends to be under exposed.
This great video from Creative Live gives a great detailed explanation of the histogram.