Here's an big picture view of why we get fat and how high intensity exercise and a ketogenic, low carb diet can help with fat loss.
(click picture for larger image as you read explanation below..)
When you eat food and especially carbohydrates, your body uses a hormone called insulin to store the glucose (sugar) that is made from the foods you eat.
If you eat lots of carbohydrates, lots of insulin is released to quickly remove the sugar from the bloodstream into your cells where it can be stored.
This is a critical function because large amounts of circulating glucose can damage your body via a process called glycosylation. Imagine what maple syrup would do if it was poured on your computer's inner circuits. All the working parts would get super sticky and stop functioning correctly. So insulin's job is to move that sugar out of your bloodstream and into storage as a molecule called glycogen.
However, the human capacity to store carbohydrate as glycogen is limited to about 270 grams total. A small part is stored in the liver to be used by the brain, and the larger part is stored in our skeletal muscles as glycogen fuel reserves.
This muscle based fuel is meant to be a sort of "turbo charge" in a "fight or flight" situation. However, if you don't use this "turbo" fuel, it stays in the muscles. Once the limit is reached, your glycogen "tank" is full and no more glycogen can be stored there.
When the glycogen tanks are full, the cells of your liver and muscles put up a "stop sign" to insulin and refuse to take in any more glucose or make any more glycogen.
They do this by "downgrading" or desensitizing the insulin receptors on their cellular surface. The result is that they stop listening to insulin. Medically, you become insulin resistant. Unstored glucose starts to build up in the bloodstream, and more and more insulin must be secreted to move the glucose.
Since the glycogen tanks in the liver and muscles are full, your liver has to send the excess glucose to your fat cells to be stored as body fat. (The liver can also make the glucose into LDL cholesterol, which is why a high sugar diet is detrimental to heart health).
As you continue to eat a high carb diet, glucose and insulin levels increase, and so does fat storage. And when insulin levels remain high, none of that stored fat can get out of the cells to be burned off.
In effect, for people who are intolerant of carbohydrates, high glucose = high insulin = high body fat.
If this condition of having to store excess carbohydrate as fat continues, eventually you develop Metabolic Syndrome, a condition in which high glucose and high insulin lead to rampant obesity, and/or metabolic issues such as diabetes.
You can now see how reducing your carbohydrate intake reduces the stress of storing excess glucose within your body, and why excess carbohydrate consumption, even from "healthy" complex carbs, contributes to why we get fat.
If carbohydrate intake is lowered, then less blood sugar is made, less needs to be stored, less insulin is secreted, and less fat is created.
In addition, another factor that plays into the process of why we get fat is the ability to EMPTY the glycogen tanks in your muscles.
Emptying those muscles of glycogen allows the receptors on the muscles cells to once again become sensitive to insulin. As the muscle cells become more sensitive to insulin, and carbohydrate intake is reduce, insulin levels begin to decline. In effect, LESS insulin is needed to store energy.
As insulin declines, and less carbs are consumed, your body can then access the fat stored in your fat cells and fat storage is turned into fat usage.
Exercise, in general, will utilize some of the stored glycogen in your muscles and provide some help with insulin sensitivity issues.
However, high intensity interval training has a stronger effect on insulin sensitivity, because it has the effect of causing your muscles to dump large amounts of glycogen. In addition, if you pair a high intensity exercise program with low carbohydrate intake, more fat will be released for fuel, and insulin levels will drop further. See this study.
More on Insulin Resistance and How To Reverse It