Obadiah is the shortest book in the Old Testament, with only 21 verses. The prophet may not have actually been named Obadiah. That word means "Servant of God" and in Arabic the same title is Abdullah. A tradition in the Talmud is that Obadiah was a convert to Judaism from the Edomites, so it is poignant that he chose to direct his invective against his native people.
The Edomites were the descendants of Esau who were the Jews' first cousins, sharing Isaac for a forefather, just as Arabs are Jews' second cousins because they share Abraham for a forefather.
The Edomites were a tiny nation that lived along the cliffs and mountaintops of the arid land south of the Dead Sea, all the way to the Gulf of Aqaba on the Red Sea. There was very little in the way of arable land, so the Edomites made their living supporting (and controlling) the main caravan route between Egypt and Babylon that passed through their whole land.
Throughout most of the history of Judah, Edom was controlled absolutely from Jerusalem as a vassal state, much like the way Syria controls Lebanon today.
Among the heathen great powers Edom was held of no account. Obadiah said that the high elevation of their dwelling place in the mountains of Seir had gone to their head a little bit, and they have puffed themselves up in pride.
"Though thou exalt thyself as the eagle, and though thou set thy nest among the stars, thence will I bring thee down, saith the LORD."
In 597 BCE Nebuchadnezzar II sacked Jerusalem, carted away the King of Judea and installed a puppet King. The Edomites helped Nebbie loot the city, and that is why Obadiah, writing this prophesy around 590 BCE, is so bitter.
"In the day that thou stoodest on the other side, in the day that the strangers carried away captive his forces, and foreigners entered into his gates, and cast lots upon Jerusalem, even thou wast as one of them."
Objectively, it is difficult to blame Edom for joining in the fun a little bit after centuries of rule by Judah. Still, Obadiah says they should have remembered that blood is thicker than water.
"Thou shouldest not have entered into the gate of my people in the day of their calamity; yea, thou shouldest not have looked on their affliction in the day of their calamity, nor have laid hands on their substance in the day of their calamity."
Never mind that other prophets were saying that the sack of Jerusalem was God punishing Judah for disobedience. Edom should not have helped God punish Judah, and for doing that, Obadiah said God will wipe out the house of Esau forever, and not even a remnant would remain.
Unfortunately he didn't tell Amos, who said in Amos 9:12 that a remnant of Edom would remain to be possessed by the Messiah, along with all the heathens. Edomites were too closely related to Judah to be called heathens even if Obadiah was angry with them.
Obadiah said the Edomites' land would be possessed by Egypt and they would cease to exist as a people. But the Day of the Lord was at hand for all nations, and someday the Jews would return from their exile and possess the land of Edom.
"But upon mount Zion shall be deliverance, and there shall be holiness; and the house of Jacob shall possess their possessions."
After the Day of the Lord (the thirty-one year period in the 20th Century from 1914 to 1945), Obadiah's prediction that the Jews would possess Edom came partly true. The western half of Edom is the Negev desert all the way to Eilat, all part of modern Israel. The eastern half is possessed by the Hashemite kingdom of Jordan.