What does motion for authority to revoke disclaimers mean

It means that a Beneficiary has signed a written 'Disclaimer' (saying 'No Thanks') to an Inheritance, and now (apparently) has changed his or her mind and by the Motion submitted before the Court is asking permission to revoke the previous Disclaimer. Similar to saying "No Thanks - But Wait I've Changed My Mind."

it means that whomever made the disclaimer (rejection of inheritance) has changed their mind, lacked the ability to disclaim (already accepted the proprty or the disclaimer was untimely) or perhaps lacks capacity to disclaim, in any case they want the disclaimer undone