SAU was the father of Edom and Edom lay close to the Jew's land. They lived to the southeast of Judah on the southern border of the Dead Sea. Of course, we know that they were close to Israel in another way. Of all of the ethnic groups in the whole world, the Edomites (descendants of Esau) were the closest to being Jewish (without being Jewish). They had a common ancestor, Isaac. Isaac was the father Jacob and Esau. Jacob became Israel, and Esau became Edom (also called ldumea). But that is where the commonality ended. Israel became a great nation with many godly citizens throughout its history: Joseph, Moses, Joshua, Gideon, Samuel, David, Solomon, Daniel, Ezekiel, Jesus, etc. Edom became an ungodly nation who hated God and hated His people. So, what did they see? Judgment! (see also Ezekiel 35)
While God did give land to Esau (see Joshua 24:4), he also rejected him and his descendants (Romans 9:11-13). Here in Obadiah, God declares great wrath against Edom. While they were only a small nation (when compared to the nations and empires that surrounded them) they received some extra attention and scrutiny from Jehovah (Obadiah 1:2). Perhaps it is because of their geographic and familial proximity to Israel. Of all peoples, they (and to a lesser degree the Moabites and Ammonites to their north) should have been most familiar with Judaism, and with the true doctrines of Jehovah. They should have been proselytes. But they were not. They were heathen. So, a whole book (albeit a short one) is devoted to their condemnation.