High Dynamic Range (HDR) photography is a technique used to improve the dynamic range (think of this as seeing more shadows and highlights) than is possible with typical film and single-image digital photography.  Typically our eyes can see a wider range than the camera can.  Have you ever taken a picture of someone that is silhouetted by the sun or a bright light?  All the features of the person are lost.  HDR would allow you to combine the brightness of the sun with the features of the person into one image.  Some smart phones today use this technology seamlessly.  You can read more about this technique here.