Who were the Eimim, and why were they so-called?
Rashi: The 'Eimim', who were originally called Refa'im, 1 lived in Ar before Mo'av expelled them and took over their land. The Mo'avim called them Eimim on acount of their dread (Eimah) which gripped whoever saw them.
Ramban: The Eimim are synonymous with the original Refa'im. 2
Why does the Torah mention the Eimim here?
Rashi: To point out that Mo'av is not the land of the Refa'im that Hashem gave to Avraham. If it were, He would not have given their land to the sons of Lot.
Ramban: To teach us that, since Hashem gave the land of the Refa'im to Avraham, it ought really to have gone to Yisrael, only Hashem gave it temporarily to Mo'av.
Seforno: To teach us that, although the B?nei Lot were not heirs of Avraham, Hashem nevertheless gave them part of Avraham?s inheritance ? like he gave to the sons of Eisav ? and to prove it, they both conquered their land in a miraculous manner.
Oznayim la'Torah: To teach Yisrael that the Mo'avim had to fight for their land - and by the same token, the B'nei Eisav had to fight the Chori for their's, 1 and that consequently, Yisrael need not be upset if they too will have to fight in order to inherit Eretz Cana'an.
As stated in Pasuk 12.
