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HDR = High Dynamic Range. It can refer to how graphics cards render images or how TVs/monitors display images. All three devices make images by using three different colors, for each pixel shown: red, green, and blue (called color channels).

Because this information is digital, each color is represented by an 8-bit number, given a possible range of 256 shades of red, etc. 8-bit color is sufficient to have almost 16 million shades of color. High Dynamic Range uses more bits for each color, usually 10-bits.

This means each color channel can have 1024 shades, resulting in smoother transitions between the colors. It doesn't actually give you 'more' red or blue or green, just more a realistic representation of that color actually appears. For TVs and monitors, though, using more bits for color channel helps to separate the differences between darkness and brightness better.