There is a process called "hydrogenation", where they stabilize the oils to make them last longer. This increases shelf life and the biggest drawback of this is the introduction of trans fats. It is basically a chemically altered mono/poly unsaturated fat, which is not a good fat. It tremendously increases the risks of heart attacks. See here for more details: http://en.wikipedia.org/wiki/Trans_fat
Whenever this hydrogenated / partially hydrogenated oil is used for frying chips or they are incorporated in the cookies, you will have trans fat in them. Of late, most of the cookies / chips makers have stopped using these oils and hence 0 trans fat. This however doesn't mean it has no fat, it just has no trans fat :)
You are starting to see No TRANS fat labels more on food, because it used to be used often for processed food. Trans Fats extend the shelf life of a product. Studies of trans fats in the foods we eat have proven to cause higher risk of heart disease and type 2 diabetes. A lot of the fat free food craze introduced trans fats into processed items on the shelf and also restaurants could purchase trans fats by the block and use it for longer in the kitchen. NY has banned trans fats from being used in restaurants, and more and more companies are claiming they remove trans fats from their products, but the FDA still allows a small percentage .5 gm of trans fat per serving and round down to zero. If you just have these type of items every now and again, it's no big deal. You are better off baking your own cookies to be sure they don't contain trans fats. Cheers to your health!