Haman was the key instigator in the Purim story and is descended from Amalek. He attempted to trick King Xerxes into thinking that Mordecai was a traitor. Upon finding out that Haman was lying, Xerxes ordered Haman hung from the gallows that had been built for Mordecai, which was 50 cubits (about 80 feet) high.
To hang higher than Haman is a phrase that has come to mean someone who has committed an act so atrocious that they are in for a very terrible punishment.
