When King Aḥashverosh appointed Haman as his Chief of Staff he ordered all the officers of the King's court to bow-down to him. Everyone did, except Mordekhay. As we explained yesterday (here) Haman's reaction (his personal revenge!) to Mordekhay disobedience was the plan to execute all the Jews.
We know of other occasions in which Jews have bowed down to others as a signal of respect. So, why Mordekhay refused to honor Haman? The key to understand Mordekhay's disobedience seems to be the word: "kore'im" (Esther 3:2) "everyone knelt and bowed down to Haman". In the Tora the verb leahishtaḥavot (bowing down) is applied mostly in the context of prostrating in front of God. But we also find many times in the Tora that Jews bowed down to other people as an expression of respect. Abraham bowed down to the Hittites, Ya'aqob to Esav and Moshe to Yitro. What we never find, however, is that people kneeled down to other people for respect. Knelling down (keri'a) has a religious connotation. As an expression of honor, kneeling down is an act of religious worship. We say in 'alenu leshabeaḥ that we reserved "kneeling down" exclusively to HaShem (ki LEKHA tikhra' kol berekh)!
As our Rabbis explained, kneeling to Haman (or to the idol he was carrying) was an act of idol-worshiping. Mordekhay was following the example of Ḥanania, Mishael and Azaria, the three Jews that 100 years before him refused to kneel down to worship Nebuhadnezzar statue, and were condemned to death. Mordekhay assumed that, same as Nebuhadnezzar, King Aḥashverosh will order his execution as well. Mordekhay was ready to sacrifice his life ('al qiddush haShem) to avoid idolatry, setting the example to all the Jews.
READ HERE the story of Ḥanania, Mishael and Azaria, called by their Aramaic names: Shadrach, Meshach, and Abed-nego.