When you perform physical activity, especially in the fasted state, your pancreas secretes glucagon which is the hormone required for you to tap into stored energy and use it for fuel. That is how you use stored fat and/or glycogen for energy.
That is also how you can go for a long time without eating. Glucagon must be secreted in order to keep your blood sugar at normal levels. Then, as mentioned above, when you exercise more glucagon is secreted and your blood sugar goes a little higher.
As a side note, this is pretty much why just about everything people have been teaching each other about meal frequency for decades has been flat out wrong. Everyone thinks that you need to keep on eating frequently (such as every few hours) in order to keep your blood sugar at a normal level. But this is flat out wrong. Because your blood sugar should stay relatively normal when you don't eat at all. And that's why you don't have to eat all day.
Such a realization should be pleasing to know for any diabetic or anyone who is concerned with keeping their blood sugar levels in check for the most part. It pretty much means that if you eat less total meals per day it makes it a lot easier. You only need insulin when you eat. So for the normal healthy person, less total meals per day means you'll be less likely to overwork your pancreas (providing you are eating a reasonable amount of calories and not too much). And for the diabetic that means less total insulin shots required per day, which decreases the probability of making a mistake, shooting too much and passing out. Sure, with such a strategy you run the risk of your blood sugar temporarily going too high after a meal (because the meals are big), but the rest of the day your blood sugar will remain stable because of the glucagon.