What does Obadiah 1:6 mean?

Esau was the brother of Jacob. Jacob's descendants became the nation of Israel. Esau's descendants became the nation of Edom. Part of Edom's arrogance came from their easily-defended homes. As alluded to in verse 4, the Edomites lived in high caves in the mountains of Seir. That kind of terrain is extremely difficult to attack, let alone "pillage." And yet, as this prophecy states, that is exactly what will happen. According to history, not long after Obadiah was written, Edom was attacked and conquered by Arabic raiders.

The book of Malachi, written after this attack, indicates that Edom's cities are now ghost towns (Malachi 1:3–4). All of the well-defended caves were empty. The riches of Edom now belonged to someone else.

This verse, along with verse 5, is not only a prophecy. It's also an accusation against Edom. When Jerusalem was attacked and looted by a foreign army, Edom joined in the attack. They looted Israel. As a result, part of Edom's judgment will be getting what they gave to others.