Calories is a measure of energy. Your body uses energy to do anything. If you do more work you use more energy. So the chemically stored energy is used to do work it can power your muscles to exert a force.

So you care about how much energy you use per unit of time. Its power. Running at a certain speed will require E amount of energy per t unit of time so you need P amount of power to run. So P×T where T is the duration of your run equals E_tot the total energy you used.

We can get energy into our body by eating. The food contains E_in amount of energy and you burn E_out amount of energy if E_in/E_out = 1 your weight doesn't change if its >1 you take in more than you use so you gain weight, if its <1 you lose more than take in so you lose weight.

Of course measure how much power is required for an exercise isn't easy but there are estimates that can be looked up. The amount of energy you need to run a distance depends on your mass and the time it took. More mass more energy less time more energy. So work would look like this W ~ m/t × d if you needed less time you had to apply a larger force and for more mass you also had to apply a larger force and the longer distance you run you need more energy. The fine details of energy consumption is in your muscles.

The point is if you eat less you will only loose weight if you use more energy a healthy adult need roughly 1500-2000 kcal a day if you exercise more than the average with that kind of consumption you will loose weight. Of course the fastest is to eat little and exercise a lot. The difference of E_out-E_in=DE and thid DE will come from your storage, fat mainly.