Who are "ha'Ratzim"?
Rashi: They are those who ride on the horses. They were commanded to run (go quickly).
What are "[Rochevei] ha'Rechesh"?
Lekach Tov: They are horses.
Ibn Ezra: They are [horses] from the king's property. There are none like them!
Manos ha'Levi (R. S. Alkavetz) #1: Rochevei ha'Rechesh is riding with extended thighs; some ride on horses with bent thighs. Rechesh are small horses; they are for far places. Susim are big horses; they are for close places.
Manos ha'Levi #2: Rechesh are small camels. They can go 100 Parsa'os in a day 1 . They are for distant lands.
Ohr Chadash: They are professional [riders]. They can go very fast.
Normally, a person walks 10 Parsa'os in a day (Pesachim 93b). .
What are "ha'Achashteranim [Bnei ha'Ramachim]"?
Megilah 18a: Even we (Chachamim) do not know what this means. (Even so, we fulfill the Mitzvah of Keri'as ha'Megilah.)
Lekach Tov: They are Chashim (rush) and run quickly Lasur 1 (to travel) to where they are commanded.
Rashi: A species of camels that run quickly.
Ibn Ezra: They are mules born to female horses [from male donkeys]. They are stronger than mules born to female donkeys [from male horses].
I.e. the word Achashteranim is based on Chash and Tur. (PF)
Why did they go on fast animals?
Rashi (14) says that Mordechai wanted his letters to arrive before the first. Fast animals are helpful for this! (PF)
Vilna Gaon: [To arrive quickly,] lest Yisrael worry too much.
Malbim #1: The messengers were tired from their journey.
Malbim #2: Until the messengers arrive, Yisrael were in great affliction. He rushed to save them.
