Public pools. Gyms. Resorts. It's common to see "no tattoos allowed" signs at establishments like this. In Japan, there is certainly a stigma towards tattoos. But why?
The easiest explanation, of course, is that Japanese gangsters (the yakuza) traditionally mark their bodies with tattoos. But not everyone who has tattoos in Japan is in organized crime. Regular folks have them. Celebs, too. Some have them for the same reasons that people do in the West, whether that's fashion or simply because they are interested in body art. And this stigma isn't a recent phenomenon.
Note: If you have tattoos and are planning on visiting Japan, you might run into problems at, for example, hot springs and public pools. Either cover your tattoos with bandages or band-aids (if possible!) or rent rooms at hot springs that come with a private bath. For business trips, unless your work is connected to the arts, it might be good to discretely cover your ink (if possible).