The pictures that move are called animated gif's. Basically .gif image files that are animated. I have no idea where most of the ones I recieve as text messages come from, as they've usually been forwarded many times between a bunch of friends, the same way jokes are.
I know of some sites that have funny/disgusting/pornographic/crazy animated gifs, but most of the time you can't send those as picture messages via cellphone because they are over the file size or image size limit.
Good luck on your hunt.