"Return, you Israelites, to the One you have so greatly revolted against. For in that day every one of you will reject the idols of silver and gold your sinful hands have made." NIV translation
Isaiah calls the people of Jerusalem to repent and put their trust in the Lord. He sees the fact that, when Jesus shows up to defend Jerusalem, the people will realize that He is the Lord and they will turn from their idols.
That battle will demonstrate to the entire world that there is only one true God and that He is in control of all things. This will set up the one thousand year reign of Jesus Christ in Jerusalem.
"'Assyria will fall by no human sword; a sword, not of mortals, will devour them. They will flee before the sword and their young men will be put to forced labor. Their stronghold will fall because of terror; at the sight of the battle standard their commanders will panic,' declares the Lord, whose fire is in Zion, whose furnace is in Jerusalem." NIV translation
The events described here is exactly what happened when the Assyrians marched on Jerusalem (see 2 Kings 18:35). The angel of the Lord went into their camp and put to death a hundred and eighty-five thousand men. They then withdrew back to Nineveh just as God promised here.
So, what does it mean when it talks of the fire in Zion and the furnace in Jerusalem? Fire and a furnace speaks of refinement and making something pure. Why did God take care of the Assyrians? He did it to refine the faith of the people of Jerusalem and the same type of thing will happen in the last days.
It is just amazing that all it takes is a tiny amount of faith and that is given to us by God. That little bit is refined and grown as we see Him at work in the situations that we face.