HDR stands for high dynamic range; and the abbreviation is often used in a longer form, HDRI – high dynamic range imaging. HDR is a form of photography that enables you to create a picture with a greater dynamic range than is usually possible.
To understand what it is and to appreciate its use, you first need to have a grasp of what dynamic range is all about.
Dynamic range is a measure of the range of different light levels – from the darkest black to the brightest white – that can be recorded or displayed by a device. It defines the amount of contrast you can capture or show without losing detail at the extremes.
The dynamic range that can be captured with your SLR is greater than can be displayed on your monitor.(http://www.digitalcameraworld.com/2013/03/02/what-is-hdr-everything-you-ever-wanted-to-know-about-high-dynamic-range-images/)
High-dynamic-range imaging (HDRI or HDR) is a set of techniques used in imaging and photography to reproduce a greater dynamic range of luminosity than is possible with standard digital imaging or photographic techniques. The aim is to present the human eye with a similar range of luminance as that which, through the visual system, is familiar in everyday life. The human eye, through adapation of the iris adjusts constantly to the broad dynamic changes ubiquitous in our environment. The brain continuously interprets this information so that most of us can see in a wide range of light conditions. Most cameras, on the other hand, cannot.(https://en.wikipedia.org/wiki/High-dynamic-range_imaging)
HDR images can represent a greater range of luminance levels than can be achieved using more ‘traditional’ methods, such as many real-world scenes containing very bright, direct sunlight to extreme shade, or very faint nebulae. This is often achieved by capturing and then combining several different narrower range exposures of the same subject matter. Non-HDR cameras take photographs with a limited exposure range, resulting in the loss of detail in highlights or shadows.
The two primary types of HDR images are computer rendering and images resulting from merging multiple low-dynamic-range (LDR)or standard-dynamic-range (SDR)photographs. HDR images can also be acquired using special image sensors.(https://en.wikipedia.org/wiki/High-dynamic-range_imaging)
Due to the limitations of printing and display contrast, acquiring an HDR image is only half the story; one must also develop methods of displaying the results. The method of rendering an HDR image to a standard monitor or printing device is called tone mapping. This method reduces the overall contrast of an HDR image to facilitate display on devices or printouts with lower dynamic range, and can be applied to produce images with preserved or exaggerated local contrast for artistic effect.(https://en.wikipedia.org/wiki/High-dynamic-range_imaging)