The term Agagi means "Agagite" — a designation used for Haman in the book of Esther. It links him to Agag, the king of the Amalekites whom Saul failed to destroy.
Haman the Agagite represents the continuation of Israel's ancient enemy, the Amalekites. Saul's failure to obey God's command to utterly destroy Agag (1 Samuel 15) had long-range consequences — Agag's descendants became agents of Israel's near-extinction. The book of Esther shows that God's purposes cannot be thwarted: Mordecai the Benjaminite (from Saul's tribe!) defeats Haman, completing what Saul left undone. Delayed obedience has generational consequences; so does delayed faith.