HDR stands for High Dynamic Range. High Dynamic Range refers to contrast and color within a still or moving image. With an HDR picture, there is a far greater contrast between the brightest and darkest elements, providing a greater sense of depth. At the same time, color range is expanded to give a much more vibrant picture.
HDR has been a common feature in cameras and smartphone cameras (if you have an iPhone, try experimenting with the HDR functions to see the difference) and is now becoming a standard feature in televisions and other display units.