Accepted means your tax return is now in the government's hands and has passed the initial inspection (your verification info is correct, dependents haven't already been claimed by someone else, etc.).
After acceptance, the next step is for the government to approve your refund.
First, they look for things like back taxes and unpaid child support. If they find any debts, they'll offset (reduce) your refund to cover the outstanding amount. Once they are satisfied that you have no outstanding debts, they will approve and then issue your refund.
Think of the e-filing/refund process along the lines of applying for a job; although the employer (government tax agency) has received (accepted) your job application, they still have to review (approve) your application before they grant you an interview (refund).
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