I'm not a nutritionist, but the theory as I understand it is that shifting the balance of calories away from carbohydrates primes your metabolism by changing the pattern of insulin secretion, making your body more likely to break down its stored fats in order to keep blood glucose levels up.

High-fat, high-protein foods also tend to feel more filling for a given number of calories, and leafy vegetables are physically bulkier, which might also contribute to their perception as less fattening.