When a nutrition label says "not a significant source of trans fat, saturated fat, etc," it does not necessarily mean that the product is fat free. It usually means that the product contains less than 1 percent of trans fat or saturated fat. Let's say you have a 10-gram cookie that has .00025 g of trans fat. That .00025 grams of trans fat constitutes only .0025% of the cookie's total weight. So, the cookie itself is not a significant source of trans fat, meaning that the cookie may have trans fat, but not a lot.
You need to be careful when reading nutrition labels. Many companies like to list nutrition facts by serving size, and this can be very misleading. Too many people think that 1 burger or 1 cookie = 1 serving, when in fact a burger can have 2 or three servings. So just a friendly word of advice: when you're reading a nutrition label be sure to make a note of the serving size. If one serving is 8 ounces, and you're eating a 24-ounce burger, then you've just eaten 3 servings. That means you have to multiply everything on the nutrition label by 3.