Proceedings Supplemental are sort of a "trial after the trial" where the winner of a lawsuit brings actions to enforce payment of his judgment. This is where a judge will order bank accounts seized and frozen, wage garnishments, and other things which enable money judgments to be collected more or less against the will of the loser.
A "Motion to Vacate" is a request for the judge to call something off, or undo something already done. For example, you can ask a judge to vacate (undo) a prior decision.
A Motion to Vacate Proceedings Supplemental is most likely a request for the judge to halt the existing proceeding supplemental, or undo orders that may have already been entered, or both. It will depend on what is actually IN the motion, and not just the title of it. It may mean that the judgment has been paid, and the person seeking payment doesn't want to go through with the hearing.