When an old movie is remastered in HD typically the company producing the remaster goes back to the original film print and re-scans all the film frames in a high resolution format. The digital files are then cleaned up (dust, dirt, scratches, etc.) and sometimes effects or transitions are recreated digitally. The resulting image is much cleaner than the SD copy which was made with older technology. In most cases this looks way better than the old version and occasionally even better than watching the film print.