What is the white soft pad under the saddle called?

It's called a saddle pad and it's there for the horses comfort. So your horse doesn't ride with a hard saddle on its back, your horse has a nice comforting pad underneath. It also does protect your saddle from sliding, because when your horse sweats it would fall off. It's all a matter of how tight your cinch is though. The cinch is the part that goes under your horses belly and you can adjust how loose or tight you want it to be. That, is the part that keeps your saddle from sliding. Anymore questions? Please contact me :)