What is the significance of Damascus in the Bible?

"See, Damascus will no longer be a city  but will become a heap of ruins (Isaiah 17:1)." This prophecy has never yet been fulfilled. It has to do with end-time prophecy. See Israel invasions and wars.

Interpretation 1: military conflict at the beginning of the tribulation
It is notable that Syria (or its ancient name Aram) is not listed among the Russia-Iran allies which will attack and invade Israel in Ezekiel 38 (Ezekiel war). It may be this prophecy concerning the destruction of Damascus will be fulfilled just prior to the Russia-Iran invasion, or could even possibly be the catalyst for this coming Russia-Iran invasion of Israel.

Interpretation 2: military conflict at the end of the tribulation
It could well be that the destruction of Damascus is part of God's wrath upon the nations at the end of the tribulation. Then the battle of Armageddon takes place, where Jesus at His second coming will defeat the armies that attack and invade Israel.

I personally lean to the second interpretation.