
That is the histogram and the corresponding image, it is an indispensable photographic tool. First off, the camera's LCD is inaccurate and should
never be trusted to judge the exposure of an image or sharpness (but that's for a different JFTP) as it is very inaccurate in colour reproduction and is not colour calibrated. Now, you're probably wondering what the heck that has to do with the histogram, well it has a lot to do with it. Most modern cameras have a histogram, on mine it was enabled be pressing the "info" button a couple times on the image review.
That presents you with something that looks like the above, it will be different for every image, but we'll use this as an example for now. I labeled the histogram with "shadow/dark", "midtones", and "highlights". The histogram tells you how many pixels are what intensity of grey, the further left, the darker the pixel, the further right, the brighter the pixel. The higher the graph goes, the more pixels are that shade of grey, so in the example image you see that there are a lot of midtones, that is denoted by how high the curve goes in the midtone section. The curve trails off before the highlights, so there are no highlights in the image at all. A keen observer might've noted that the curve is cut off on the left, that means that those pixels are pure black, or in other words you have no data there whatsoever.
That brings me to the next point, the histogram represents the latitude of the image, or how much will be shown with acceptable contrast. What that basically means is that if all of your data is to the left (ie not able to be shown on the histogram), you have a pure black image with no data whatsoever, if all of your data is to the right then you have a pure white image. How this relates to your everyday image usage and editing is; if your data is clipping (the term used for when colors are outside the latitude of the image) then you will not be able to bring it back, even if you use photoshop.
Here is an example of both of the extreme ends of the histogram with the corresponding images.

Now you see both histograms are clipping to an extreme amount, that means that neither image will be salvageable. You've probably had an extremely overexposed image or underexposed image that you thought you could bring back using photoshop or some other program, but found it wasn't possible. That was due to clipping, if you look at the histogram it will tell you whether or not the image is salvageable. One more thing that should be mentioned is that the the camera is showing you the JPEG histogram (even if you shoot RAW), with RAW you will have more data, but do not trust this enough so as you don't shoot another better exposed image.
Anyways, that's the basics of the histogram, as always if you have any questions whatsoever just leave a comment or a note and I'll get back to you on it

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