Can you please clarify. Did both returns got accepted by the IRS?
Sometimes you can claim a dependent over 18 that is a full time student and that you still provide more than 50% of their own support, and then the dependent will still file their own Tax Return "as a dependent of another return". If this was the case, it is totally acceptable and you do not need to take any further action.
If you included that dependent on your return, and the person tried to file their own separate taxes (not as a dependent) it will get rejected by the IRS. You will then need to file an amended return to remove that person, and your dependent will need to submit his/her own taxes by paper, as it will not let them file electronically.
