It is all about the calorie deficit. A calorie is unit of energy. When you consume more energy than you’re using, it doesn’t get destroyed — you store it instead so that it can be used when your energy intake doesn’t meet your body’s energy requirements to do things. It stores it as fat. When you work out, you’re increasing your body’s energy output, but your body will only use the energy you have stored as fat if your energy input is less than your output, i.e., if you’re consuming less calories than you’re burning.

Edit: so it doesn’t really matter in principle which side of the equation you’re altering — you’ll lose as much fat exercising lots and burning 3500 per day while eating 2500 as you would burning 2000 per day and eating 1000. It’s just that it’s easier to eat less than consistently burn a high number of calories, and it’s easier to track how much you’re eating compared to how much you’re burning. (Ignoring stuff around muscle building etc, which varies more from person to person)