Burning Fat
The phenomenon of excess carbohydrates in the diet preventing fats from being used for energy is especially true before an exercise and especially competition. For example, taking a high carbohydrate food or drink before your workout or race can have devastating effects for the reasons described above. Keeping those substances to 3% glucose or less will keep you away from danger. (Eating or drinking high carbohydrates during your workout or race will not create the same problem as taking them before.)
The training aspect of burning more fat and less carbohydrate is also very specific. The aerobic muscle fibers (the so-called "red" or "slow-twitch" muscles) generate energy by burning fats. This is accomplished in the mitochondria, found within the aerobic muscles. As these muscles are trained they become more capable of converting fats to energy - as long as insulin levels are not too high. Relatively slow rather than fast training provides maximum benefits to these anaerobic muscles, training them to burn more fat for energy. As you develop the aerobic muscle you will burn more fat and your pace, or speed, will get faster, as will endurance.