What does Obadiah 1:17 mean?

Just as Mount Esau and Mount Seir are metaphors for Edom, Mount Zion is a metaphor for Israel, specifically Jerusalem. The term "holy" means "set apart," often applied to the nation of Israel. Instead of being scattered, Israel is prophesied to finally take back her Promised Land. "The house of Jacob" is another reference to Israel.

This is another common aspect of Old Testament prophecy: the mercy of God. Instead of simply destroying all sinners, everywhere, God extends mercy to those who obey Him. Israel was often reminded that their survival was not because of their own merits, but because of the mercy and judgment of God (Deuteronomy 9:4–8).

The nation of Edom was completely destroyed when God judged them. The nation of Israel, in contrast, survived and exists to this day (Amos 9:8; Malachi 2:1–5). While some descendants of Esau are, presumably, still on earth, the next verse seems to suggest that none of these will survive into the millennial kingdom. Prior to the end, the lands which once belonged to Edom will be occupied by the children of Israel (Amos 9:12).