a paper towel, napkin, tissue or other disposable article used to wrap the bangin' sandwich you just made in place of using a plate. typically used because you are too lazy to wash dishes or too poor to afford them in the first place.
Jess: "wow i'm making a really good sandwich."
Sherri: "do you want a plate to enjoy your delicious creation of culinary genius from?"
Jess: "no, i'll just wrap it in a sandwich diaper. i'm much too baked to wash dishes tonight."