Do bicycle crunches and sit-ups actually burn fat or only enhance your muscles?

Multiple benefits. Sit-ups take some energy to do and that means you use calories. If you use more calories than you take in, you will "burn fat." it's that simple. Crunches and sit-ups selectively enhance abdominal muscles and increased muscle mass means you use more calories than say an equivalent amount of fatty muscle. So do sit-ups if you a) want six packs and b) need to burn more fat.