While many of the Old Testament prophets address nations other than Israel and Judah to some extent, Obadiah is somewhat unique in that his recorded prophecies are all directed at a foreign power: Edom. The Edomites were descendants of Esau, the brother of Jacob. The tension between the brothers continued and worsened through the generations.
Obadiah delivers an indictment against Edom because of its haughtiness and the way it gloated over the fall and hardship of Israel. Rather than seeking peace with their neighbors, ostensibly their long distant cousins, they were belligerent and delighted in Israel’s subjugation to foreigners.
The judgment of Edom would come in the form of its own fall and eventual obliteration as a nation. The territory of Edom would be possessed by Israelites returning from captivity.