Without going into full audiophile mode, let me explain. In the early days of recording, mixing, and mastering digitally, there was a loss of resolution at each step, so the final product was crappy in quality. Add to that the super-cheap electronics they put in the CD players, and the result was worse than good analog. It's a lot like making enlargements from early digital cameras, or seeing artifacts on an LCD TV.
Digital recording and playback eventually surpassed analog, but there's still a difference between cheap digital and cheap analog, with the latter sounding more pleasant and musical to many. For the most part though, people play vinyl today for the emotional experience.