What they found out was that the people who were given larger forks left significantly more food on their plates than those with smaller forks. But why would larger bites make you eat less? Because sight plays a huge role in our eating habits. We rely on visual cues to guide us when we're eating (i.e., how much food we see on the plate), since it takes our nervous system a while to realize whether we're really full or not.
So, if your senses are telling your brain that you should be satisfied, the brain will decide that, what the hell, you might as well be. When you use a bigger fork, you'll see yourself making bigger dents in the overall food on the plate, fooling your brain into believing that you're overeating. With a smaller fork, the transition from "a lot of food" to "hardly any food at all" is more subtle, so you keep on snacking well past the point your thunder thighs would appreciate.
Next thing you know, your dining room has no furniture.
However, the "use a bigger fork" trick only works at regular meal times, where your goal is to eat until you're satisfied. If you're snacking (where your goal is to eat until your pants explode), using a bigger fork will simply make you eat more food.