Dynamic range is a simple concept: it is the difference between the darkest and the brightest parts of your scene or image.
Let’s say the brightest part of your scene is a thousand times brighter than the darkest one. If your camera can record all of that, all is great, your photo will contain all the details that your original scene has. You would have nothing to worry about!
What happens, though, if your camera simply cannot record it all? And on top of that, your monitor cannot even display all the range that your camera did capture? When it’s just too much? Well, the dynamic-range giraffe is a visual metaphor that explains that to you.
(In case you’d like to see a different visual metaphor, have a look at Art Adams’ excellent article on provideocoalition.com.)
Is there a solution?
Of course, there is! Photographers and cinematographers have been using two approaches since the dawn of their trades. The first is, to modify the contrast ratio of your subject, to make the dynamic range of your scene fit the dynamic range of your negative, reversal film, digital sensor or your television screen. You need to be able to control light to achieve that and this is why so much photography is done in studios where everything is under your control.
The second solution for digital cinematographers is to use so-called gamma curves that modify how the dynamic range of your scene is ‘translated’ on your sensor. Instead of me repeating what much greater minds have said, here’s a link to a great introduction to the world of gamma curves (linear and logarithmic) by cinematographer Art Adams.