IANADietician, IANA Fat Specialist except in the sense of demostrating how to ensure I have lots.
There’s a whole series of different arguments, not unlike what St. Cad mentions.
Just after you eat, as the meal is digested, your body reacts - blood sugar rises (if it was that sort of meal) insulin kicks in, some say insulin is “bad” as it tells the body to store anything unnecessary for a rainy day (the old Atkins diet argument). 6 small meals vs. one large one keeps your blood sugar elevated for longer. Meanwhile, starch breaks down to sugar slowly, so instead of getting a blast of sugar in the blood, you get a more gradual rise and fall. Again, 6 small meals means a much longer time with elevated blood sugar.
IIRC, you have to be starving for about 2 days before your body goes into panic mode and starts shutting down unnecessary calorie consumption. This the “starve for only 2 days” diet - you are using up calories from your stored reserves, but avoid the shutdown where your body suddenly can get by on a reduced caloric intake.
(This is also the “theory” of the Atkins diet… that the mechanism that triggers the burn mode - burn calories from fat because we’re not eating any food - is triggered from lack of carbohydrates, while the starvation response - stop burning calories and shut down as much of the body as you can - comes from a lack of protein. Eat only protein - and maybe some fat - and the body will at the same time burn off fat while not severely shutting down it’s normal functions.)
Your body burns calories even at rest. One item I recall said about 1/3 of the calories we burn go to making the brain work - thus, other animals have much smaller brains because maintaining a brain is expensive, and unless it gives a good return on that investment or food is plentiful, it is a luxury that evolution may reduce. It also explains why having a good meal before taking a test is an advantage if you are typically short of nutrition.
Both the brain and the muscles burn energy, even at rest. This is another way that exercise helps. You build the muscles your body demonstrates that it has needed. These muscles burn energy just being there. So exercise helps you even when you’ve stopped. A fit person likely burns more calories.
This is also one of the dangers of starvation diets (and possibly Atkins). When the body goes into starvation mode, one way it prevents a high level of calorie burning, to survive a lack of food, is to stop feeding the rest muscles. Instead they absorb these muscles. If the diet goes too far, the body may be absorbing relatively important muscles, like heart muscle. Excessive starvation diets can result in heart problems among other problems.