Even though Esau is not a patriarch, he is still the only brother to the patriarch Jacob. He would also be the father of the Edomites, who would play a significant, albeit negative, role in Israel's history. What is more, we get another tidbit from the genealogy.

Another significant foe would arise from Esau's line, namely, Amalek of the notorious Amalekites, who would be the first to attack Israel, when God brought them out of Egypt. Amalek was the grandson of Esau:

Timna was a concubine of Esau’s son Eliphaz and she bore Amalek to Eliphaz. These are the sons of Esau’s wife Adah (Genesis 36:12).

If you would like to read more about the Amalekites and their history with respect to Israel, I recommend this article from the Jewish Encyclopedia: "Amalek, Amalekites"

What is more, some other names, like the "Horites" and "Midianites" are also mentioned in other places in the Bible.

Why does Moses give the genealogy of Esau? Everything up to the time of the Exodus was likely given to provide a history and moral instruction for those Israelites about to enter the Promised Land of Canaan.

Moses gave the background of Israel, as a people led by the grace and power of God in keeping with His unfailing promises to the Patriarchs, which God gave to raise up a people for His Name, through whom He would restore a broken relationship with His creation, which was caused by the sin of Adam and Eve.

The history of Jacob's brother Esau supplied part of the larger background of the nations that Israel would have to contend with in the years to come. Esau was the father of the Edomites.

Abraham's nephew Lot fathered Moab and Ammon, who would become the Moabites and Ammonites, just north of Edom. They too would be nations with which Israel would have to contend.

From Moses' account of Abraham's third wife Keturah, the people would understand where the Midianites, who would later precipitate the destruction of 24,000 Israelites, came from. They came from Midian, the fourth son of Abraham and Keturah.

There were other nations that came from Ishmael, Isaac's brother through Hagar.

Moses also went further back to the sons of Noah, where the people learned the origin, not only of the Jews through Shem, but also through Noah's son Ham of the people of Canaan (i.e. those that God commanded Israel to annihilate) and the Assyrians (i.e. those that destroyed Israel) and the Babylonians (i.e. those that destroyed Judah), all of whom would be serious foes of Israel.

It is sad to think that this brief history (all pretty much contained in the book of Genesis, and most in just the first eleven chapters) suggest that the history of the world is a history of brothers fighting against each other, taking each other's lands, and destroying each other, sometimes horribly.