The histogram represents the range and relative intensity of the different tones present in the image. If you take a picture of a monochromatic scene with flat lighting you will get a histogram that is a single spike in the center (in the center because the camera's meter will try to make it average to neutral gray.) If there are no shadows there will be no information in the left side of the display. If there is nothing white present in the scene there will be no information on the right side.
It is usually desirable to have a full histogram because it typically means you have a well exposed image with a wide range of tonality present. There are tricky situations where the camera meter will not make the best choice. It's your job to add some exposure compensation. Looking at the histogram will guide your choices.