Imgur user IFKTyrantr originally posted a gif of a girl working out on a yoga ball, followed by a cat walking into the frame and sitting in front of the camera.
http://imgur.com/gallery/qBtvSZs
The top comment for this post, written by muthafluffinspidaman, said “Someone needs to edit every NSFW gif and put that cat to censor”. Two users, fabrixxm and bluwoh, both created different transparent versions of the gif, and thus, SFW Cat was born.
http://imgur.com/gallery/M3zbM4X
http://imgur.com/gallery/aMHCksi
Sightings of SFW Cat in the wild:
http://i.imgur.com/LgAK7rD
http://i.imgur.com/5mMsaWD
http://i.imgur.com/5Sf5RUu