The fundamental science behind this way of eating is as follows:
The body’s primary fat-storage hormone is insulin. Insulin secretion is stimulated by a high blood-sugar level. A high level of insulin in the blood causes blood sugar to be burned in the muscles and stored as fat in the adipose tissue. Carbohydrate, being made of glucose molecules strung together, raises your blood glucose and therefore your insulin level. If you want to burn your fat, you need to keep your insulin level low. To keep your insulin level low, you need to avoid eating carbohydrate.
Protein stimulates insulin secretion, too, but it does so at half the rate of carbohydrate. So we want to avoid eating too much protein. But we have to have a certain amount of protein, or we’ll starve, so the idea is to eat a moderate amount of it—not too much, and not too little.
This means that most of our calories have to come from fat, and fortunately fat stimulates insulin secretion only a little, so it is a safe source of calories. The idea is to replace the calories no longer coming from carbohydrate with calories from fat. And a gram of fat has twice as many calories as a gram of carbohydrate or protein, so it takes a lot less to give us the equivalent amount of energy. Fat is also very flavorful and satisfying.
Finally, when insulin levels are low, the body still won’t let go of its excess stored fat, as long as it thinks there is a famine going on—and restricting calories is a signal that there is a famine. So the body needs enough energy to convince it that letting go of the excess fat is safe. And the key to that is to eat enough at each meal that you don’t leave the table hungry. And because of the insulin business, a large percentage of those calories will come from tat.
At first, this may involve eating a lot more than you think is right, but trust your body; for most people the lowered insulin allows their satiety signaling to work properly again, and in a few weeks at most, you are likely to find your appetite cutting back noticeably. This is a sign that your body is getting enough fuel. If you let it, your body will set your appetite to give it just enough food so that it can manage to burn both the fat you eat and your excess stored fat (this kind of calorie restriction is okay, because it’s the body’s idea, not ours). Eventually, you will run out of excess fat and need to get all your daily energy from the food you eat. As long as you continue eating fat to satiety, your calorie level will be adjusted automatically by the signals from your body; you won’t have to count a single calorie.