HDR is called High Dynamic Range and describes the process of creating a picture from various pictures with different exposure time, which includes the full dynamics capture of all images (ie from completely dark to very bright). This is usually not possible with a snapped image, since certain parts of the image are over-exposed or under-exposed (both of course) by the exposure. Thus, HDR images are already quite close to human vision because the eye has a very high dynamic gain relative to brightness values. Usually one makes at least three pictures, one with -2eV (ie two steps underexposed), 0 and + 2eV (that is, two steps overexposed). There are no limits to the top, of course it is also possible to make 5 or 7 pictures when the camera allows it (automatic exposure series), e.g. -6, -4, -2, 0, 2, 4, 6, etc. A corresponding software, such as Photomatix Pro, then calculates a single HDR image with the aid of various parameters which can also be partially adjusted. This image can not be seen on normal monitors, since these can not cover the high dynamic range of an HDR. Thus, with the so-called tonemapping, the image has to be converted in such a way that it is visible on normal monitors, but at the same time is taken into account by the high dynamics capture. There are pictures with an eye-opening effect. There is a drawing in black at the same time, and you can see things and structures that can not be seen in normal pictures, provided of course you have made certain settings sensibly and not extreme.
Look here for some comparison LDR-HDR.