What does 2 Corinthians 3:16 mean?

Paul has described a condition that afflicts every human being, though he is talking specifically about the people of Israel. Despite their privileged position as God's chosen people and His revelation to them of Himself through the law of Moses, they could not reach a right understanding about who God is. They could not see His glory. Paul has described this separation caused by human sinfulness, by the hardening of our minds, as a veil that lies over our hearts.

We cannot remove this veil ourselves no matter how sincerely we want to or how diligently we study or how desperately we try to obey. Our sin stands in the way, keeping us from God's glory (Romans 3:23). But, Paul now adds, when a person turns to the Lord, the veil is removed. It is replaced by the rock-solid hope of sharing in God's glory for eternity (Romans 6:23). But this veil is only removed through Christ. There is no other way to be free from it.