According to Pirkei D’Rebbe Eliezer (50) Haman intended for Achashverosh to provide the clothing he wore at his coronation. As can be seen in museums around the world, the clothes worn at a coronation or even presidential inauguration are important, and become part of the culture.
The Yosef Lekach explains that these could not just be any clothes, but had to be special and were likely kept in storage for important occasions like this.
R’ Avraham Chadidah writes enigmatically that Haman meant to imply to Achashverosh that his providing the clothes would show that he is a kind, generous man.
R’ Dovid Holtzer explains that the logic behind this depends on how the king defines himself. Achashverosh, from his original invitation of the rich and poor to his party (Esther 1:5), defines himself as a nice, generous person. Similarly, the nuance of clothing defines oneself. The clothing one wears defines one’s political beliefs, religious concerns, cultural status, etc. Therefore, dressing like Achashverosh can make you like Achashverosh in character.
On a more mystical level, R’ David Valle writes that the idea of a king’s clothing refers to the King above rewarding the righteous below. He writes that such rewards come from the forty-five letter Name of H-Shem. Forty-five is also the gematria of the word kacha (“like so”) referring to this reward in the next verse (Esther 6:9) and the gematria of adam (“man”), meaning that H-Shem always rewards the righteous, even when it is not manifestly apparent to us with our limited vision.