The histogram is affected by exposure (how bright or dark the different areas of the image are.) The histogram must not have a peak at the very far left or right side (the red areas). This means that you have lost an area of the image.
Under-exposed:
Solutions:
Use a longer exposure
Use a lower aperture (lower F-number)
Use higher ISO sensitivity
Picture can be rescued in software: Yes
Over-exposed:
Solutions:
Use lower ISO sensitivity
Use a higher aperture (higher F-number)
Use a shorter exposure
Picture can be rescued in software: No
Proper exposure:
This histogram indicates a successful shot. Other shapes of the curve can also mean a successful image, as long as there is not a tall peak within the read areas.
Proper exposure:
This image has slightly more contrast, but still not blown out. There is some energy in the red areas, but not much compared to the rest of the curve.
Too little contrast:
Solutions:
Increase the in-camera "contrast" or "tone" setting
UV filters sometimes remove a little bit of haze in landscape images, but the effect is subtle
Increase contrast using "levels" in software
Picture can be rescued in software: Yes
Too much contrast:
Solutions:
Decrease the "contrast" setting
Move to a better location
Move the light sources if possible
Shoot "raw" instead of jpeg
Get a better camera
Try old-fashioned slide film
Picture can be rescued in software: No
Having too much contrast is a serious problem because most likely you can't do anything with the camera settings to fix this. Check that "contrast" is set to normal or low, and try shooting "raw" instead of jpeg. RAW images are often able to cope with more contrast than in-camera jpeg for some weird reason.
If that also does not help, your camera is simply not able to cope with the extreme light conditions. Either get a more expensive camera or use old-fashioned dias slide film.