"Duty" is a formal, serious word. If you have a duty to do something, you have a job or a task that you HAVE to do. Your duties are the things you must do.
When you report for duty, you show up for your job. And when you're on duty, you're on the job: you're working, so you can't play around. And when you do your duties, or fulfill your duties, you do the work that you're supposed to do.
For example, if you take a job in a grocery store, your duties might include bagging people's groceries, stocking the shelves, and cleaning the floors.
If you become a parent, then it's your duty as a parent to take good care of your kids. If you become a doctor, then it's your duty as a doctor to heal people and never harm them. And if you adopt a pet, then it's your duty as a pet owner to give your pet food, water, exercise, and love.
If you're a dutiful student, then you're careful and hardworking as you perform those duties; you're responsible and respectful as you carry out all your duties. Dutiful sons and daughters do their chores, help around the house, and follow their parents' rules or instructions. And dutiful workers do everything they're supposed to, without complaining or wasting time.