HDR stands for High Dynamic Range and refers to an effect used on photos to help bring out the best possible qualities in every area of a photo. Most photos have certain areas that aren't well lit so they appear much darker than the properlylit parts of the photo, making it diffucult to see any detail in the dark areas. The big contrast in lighting also makes the photo look uneven in general.
HDR involves taking several pictures of the exact same scene, with each photo shot at different exposures (usually 3), thus creating the "dynamic range" of lighting in the photo. The first photo is taken at a low exposure creating a dark image (allowing very bright areas of the photo to look more natural), the second photo is taken at a standard exposure setting (creating a "normal" looking photo with a few dark and bright spots), and the third photo is taken at a very high exposure (which brightens up dark areas so detail is seen in those areas). The 3 photos are then combined with special software which combines the best looking parts of all 3 photos to create a a very evenly and well lit photo with details visible for every part of the photo. See some examples below!