The land of Edom lay to the south-east of Israel.
There is a long history behind the antagonism between Edom and Israel which is reflected in Obadiah.
Impulsive Esau had sold his birthright to his scheming younger Jacob. Each were given new names, and these became the name of the two nations descended from them – Edom and Israel.
After the Exodus, the Edomites would not allow the Israelites to pass through their territory (Nu. 20:14–21; Jdg. 11:17–18). Saul had fought against Edom (1 Sa. 14:47), David had been victorious in battle over it (2 Sa. 8:13–14), and Solomon had occupied it (1 Ki. 9:26–28). During the reign of Jehoshaphat, Edom and others attacked Judah (2 Ch. 20:1–2). Edom was free of the yoke of Judah for some 40 years (2 Ki. 8:20–22; 2 Ch. 21:8–10). Edom was then recaptured (2 Ki. 14:7; 2 Ch. 25:11–12), while later Edom attacked Judah (2 Ch. 28:17), freeing itself from Judah’s domination. Later, Edom became first an Assyrian, then a Babylonian vassal. Thereafter, Edom was in decline. Some of its inhabitants were forced into southern Judea, in an area which became known as Idumea (a name based on the Heb. ‘Edom’).
(Based on NBD)
The gospel in Obadiah
Like the book of Nahum, Obadiah presents something of a challenge for gospel application. But note the following:
In vv17-21 there are indications that a remnant of Edom will be saved. So also in Amos 9:11f (of which Obadiah, the very next book in the OT, may be an elaboration).
The relationship between Judah and Edom has its roots in that between Jacob and Esau. God’s sovereign grace was apparent in his choosing the younger to serve the older (Gen 25:22f;; Mal 1:2f; Rom 9:13). ‘Even though the “house” (nation and kingship) of Esau will be no more (Obad. 18), God will also graciously save a remnant of Edom for his kingdom (see above). For both the house of Jacob and the house of Esau, the blessings experienced are due only to the grace of God.’
In the New Testament, the Jacob/Edom dynamic is taken up in two ways. First, it is those who believe in Jesus Christ who inherit the promises to Abraham and his descendants (Jn 8:39-47; Gal. 3:7; Rom. 2:28; 9:6–18; cf. Heb. 12:15–17). Second, and even more foundational, it is Jesus himself who is the promised Seed of Abraham (Gal 3:14-16). Through him, all the promises of God have been, and are being, fulfilled, 2 Cor 1:20.
(Based on the Gospel Transformation Bible)