Oh, wait, now I think I understand what you're saying.
The point is that there are three energy producing nutrients in your body (carbs, fat, and protein), and the way they're utilized is dependant on the activity you're doing.
When you're just jerking around the house or at school or at work, doing nothing much at all, you're burning fat - which is used for extremely low-intensity activities. However, because these activities are so low-intensity, you're burning a negligible amount of fat. Not enough to lose weight, really.
If you want to stimulate faster fat burn, you have to do a more intense workout (thus requiring more energy, hence more fat burn). However, for high intensity exercise, your body first attempts to use carbs. Carbohydrates are a much more high-energy-yield nutrient than fat - so it makes sense that your body would save these for higher-intensity activities.
So, in order to stimulate the accellerated fat burn, you'd first have to utilize these carbohydrates.
Now as far eating fewer calories than you take in, this works on a different principle. No matter what, your body needs energy. If it requires more fuel than you put in it, it's going to tap into its stores to get at them. Body fat is stored energy - if you're not providing enough energy to the body (i.e., eating as many or more calories than the body burns in a day) then the body taps into these fat stores for energy.
