DNR stands for digital noise reduction, it's commonly used on blu ray transfers to eradicate or lessen film grain, all too often it smooths out an image and removes fine detail, another byproduct of digital noise reduction is the blur effect, all too often i notice this slight blurring effect on transfers which get high marks, take Disney animated films as just one example, many of these classic films are being repainted by Disney and the optical effects stripped clean of their original grain structure. look closer and you will also see a loss of detail to some parts of the image caused by the removal of the grain structure which was on the original film, newer Disney films from the nineties onwards would often have digital files stored in a computer so do not suffer from this blur effect, in my opinion the older classic films do suffer and are not being treated correctly by Disney. Take a look here at my True Romance comparison, the Warner edition has that blurry look indicative of heavy handed DNR.
It is possible to use other types of filters when applying digital noise reduction, Lowry do so and nowadays are able to produce some stunning results, grain removal is not always evil, sometimes it is needed when a new film scan is made and the grain structure becomes more prominent than the original cinema version, sometimes it is used to make one or two scenes look identical to the rest of the film, it's all a question of how it is used and whether it is applied with a light hand or a hard touch, poor use of digital noise reduction can often result in artifacts which were not part of the original film and such a soft picture that the studio then needs to apply a liberal dose of edge enhancement, more information on edge enhancement here.
In photography you will often find grain is unwanted, the reverse is true of cinema and movies where filmmakers will sometimes add grain for artistic reasons, you will also find it more prevalent in nighttime cinematography where a lack of light often means grainier images, try capturing a photograph at night with very little light using your digital camera and you will see much digital "grain" or as some call it, noise.
Film grain removal leads to far too many issues and should be avoided, if it must be done at all then it should be done with care and consideration, after all it is a film and even if Lowry or someone else was able to degrain the film without adding any side effects you will still be losing the film texture that separates great cinematography from bog standard digitally shot television shows, i would recommend that those who complain about film grain should turn the sharpness control down on their television/projector and get it calibrated, if they still think film grain is bad after doing this then they should find a new hobby.
Roger Deakins who was the director of photography on The Big Lebowski and other Coen Brothers films has this to say on the subject matter.
"I would prefer to scan everything at 4K these days and output the same, however, it seems some producers still want to save money by doing 2K. Personally, I think this is very short sighted and certainly does not reflect the true quality of a properly exposed film negative. I insist on 4K scans, as I like any grain that there is to be sharp and the image also. Some would say that you need a 6K scan to see the full detail/fine grain in a 35mm or anamorphic negative and I believe they would be right. The de-graining tool is really only putting the image out of focus and I wouldn't recommend it as standard. Like every tool there are pros and cons. Everything comes at a cost!"
For examples of DNR check my major issues list here and some blu ray screencaps of Basic Instinct here. DNR is a cheap way of trying to fix issues with older masters, what they need to do is actually do new film scans and treat their films and potential audience with more respect, DNR short changes us all, it robs the film of detail and it's short term thinking by whoever is making these decisions, long term it benefits the studio to invest in their history and make sure pristine prints of their film library are available for all to see. Below is an example of a great film ruined by DNR, Predator Ultimate Hunter Edition, the first image on the left is from the ultimate hunter edition, the second image is the original blu ray of Predator where Arnold looks healthy, in the ultimate hunter edition he looks like he has overdosed on botox but it's actually overuse of DNR, now sure the whole film isn't like that image below but there are enough scenes like below to take you out of the film and ruin it, film grain is vital to preserving fine detail.