Epistemic duty refers to the idea that a person must believe certain truths based on evidence available and is obligated to always seek the truth and avoid believing what isn't true. For example, if you were raised to believe that the world is flat and are confronted with evidence to the contrary, your epistemic duty requires you to reject your former belief and accept the new evidence as truth.
The question surrounding epistemic duty is that often people believe what is proved to be false even when confronted with evidence. This makes it questionable whether people have complete control over their beliefs since they often believe things for more than purely rational reasons.
The basic idea of epistemic duty remains clear no matter whether an individual has complete autonomy in terms of his beliefs. It boils down to the duty of every person to search for and believe truth and to eliminate falsehood.