Is it true that you are supposed to burn more calories than you take in a day?

Only to lose weight. Our bodies are in a simple state of balance. If we eat more calories than we use, we gain weight. If we eat fewer calories than we use, we lose weight. So, people who stay the same weight eat more than they use on some days, and less than they use on other days . . . But it averages out over time, so that they are eating & using the same number of calories. That is why their weights don't change.