A prove-up is the final part of a dissolution of marriage (divorce) or dissolution of civil union case. It is a hearing typically run by a hearing officer, who guides both parties through the process of settling on the final terms of their (marital) settlement agreement.
Prove-up hearing will only take place if the parties are ready to make a final agreement. Otherwise, a judge will order the final terms of the settlement agreement after assessing both sides of the case.