Towards the end of Parashat Vayishlach (36:20-30), the Torah presents a brief list of the families of Se'ir, who lived in the region that was ultimately captured and settled by Esav, where he established the kingdom of Edom. Today we will look at several approaches that have been taken in explaining the purpose behind this section.
Rashi (36:24) explains that this record is presented for the purpose of identifying Timna, a member of the ruling family of Se'ir (36:22), who was earlier introduced as the pilegesh (concubine) of Esav's son Elifaz. Despite Timna's royal stature, she was given as a pilegesh to Elifaz. This demonstrates how highly the people Se'ir valued the family of Avraham, as a family from the ruling class was prepared to have their daughter become a pilegesh to Avraham's great-grandson, rather than become a noblewoman among the people of Se'ir. The Torah presented this genealogy for the purpose of demonstrating the respect and fame Avraham had earned in this region even several generations after his death.
Ibn Ezra (36:20) suggests that since the Torah would later forbid instigating hostilities against the nation of Edom (Devarim 2:1-8), it was necessary to distinguish between the peoples of Se'ir and Edom. After Esav's conquest of the territory of Se'ir, one might mistake the people of Se'ir for Edomites. The Torah therefore carefully delineated the families of Se'ir so that Benei Yisrael would be able to differentiate between the Edomites, with whom they were forbidden to instigate warfare, and the people of Se'ir. A similar explanation is cited in the work Ha-ketav Ve-ha-kabbala in the name of the Vilna Gaon.
In a slightly different vein, the Rambam (Guide for the Perplexed 3:50) explained the purpose of this section in light of the command to annihilate the nation of Amalek (Devarim 25:19), which was founded by a grandson of Esav (36:12). Esav became connected with the people of Se'ir through marriage, and Esav's children became the dominant influence in the area to the point where the entire population assumed the title "Amalekites." The Torah therefore made a point of presenting the genealogy of Esav and Se'ir, so that Se'irites who were not members of the Amalekite clan would be spared Benei Yisrael's vengeance against the Amalekites.