In simple terms, HDR is a way to visualize the widest dynamic range inherent in capturing the original content. A modern film camera or digital camera can capture a higher level of brightness (luminance) and blacks considerably deeper than a current video screen can display. However, if you can create a transfer that keeps all these luminance details and a screen is able to display it, then the resulting image will be a better representation of what the human eye is able to solve.
It is important to realize that HDR is not just about increasing the brightness of an image, although this is a common misconception. The idea is to increase the overall dynamic range between black and white making the dark parts darker and the parts brighter, keeping the details when both are in the frame. So, for example, if the image was of the interior of a room you could see the details in the dark shadows, but also make details through the illuminated window.
However, it is not only the difference between the darker and brightest elements of an image, HDR also requires greater expression and detail within the colors. Therefore, HDR will use a larger color space than the current Rec.709 standard. It has not yet been announced exactly what color space will be used, but probably the DCI standard used in cinema, although theoretically it could go as wide as Rec.2020.
The current 8-bit video standard allows you to display a maximum of 256 shades of any primary color, but under the new 4K Ultra HD standards, displays will need to be able to handle colors at a depth of 10 bits, allowing 1,024 tones of each colo pr im you. Combining a wider color space and greater bit depth will result in a more natural look and detailed images than you can achieve today.
Although HDR and wider color spaces are technically separate aspects of image reproduction, the two are becoming connected by standard bodies in what is often called color volume. This is essentially a three-dimensional version of the previous chart with combined color and luminance. The greater the luminance range and the wider the color space, the greater the overall color volume and therefore the greater the impact on the perceived image.
The combination of a wider dynamic range and a wider color space results in a higher color volume and a better perceived image.