"I'm the guy who will eat something that looks nice when I'm out, but when I take it home in a doggie bag, it'll sit in the back of my refrigerator until it starts to move"

In this quote, Dustin Diamond is explaining himself as somebody who is quickly tempted by aesthetically appealing food when he is out and about. Nevertheless, when he takes the food home in a doggie bag, he loses interest and it ends up forgotten in the back of his fridge. Using the expression "begins to move" recommends that the food is left for so long that it begins to spoil and establish mold or bacteria. This quote could be interpreted as an amusing method of stating that Diamond tends to waste food or forget it, even if it initially caught his attention.