HDR stands for High Dynamic Range. It's a technique which combines multiple captures of the same image to deliver a picture with detail you cannot capture in a single image.
If you've ever tried to take a photograph of a person against the sunset, you'll know that either the sunset is washed out or the person is a silhouette. This is because cameras are limited in the range of detail they can capture in the brightest and darkest parts of an image. With HDR images, the photographer (or if the camera provides an HDR function) takes three or more photographs of the same scene, exposing one for the darkest areas, one for the mid-tones, and one for the brightest areas. These are then compiled into a single image that shows detail in every part of the image.